This illustration shows how to change or update the business unity for a systemuser / user in Microsoft Dynamics CRM 2011 in code in jscript and also C#  using the SetBusinessSystemUserRequest.   This example will be given in SOAP (JScript) and in C# (.NET).

Ok, here is what the code look like!
First in C#:

SetBusinessSystemUserRequest req = new SetBusinessSystemUserRequest();
//business unit to assign user to
req.BusinessId = new Guid("9225A2E5-4970-E011-8D78-1CC1DEE8DA78");

//user to re-assign
req.UserId = new Guid("E497532F-D37C-E011-8D72-1CC1DEE8EA49");

//can be a different team or systemuser, used to reassign records owned by person
req.ReassignPrincipal = new EntityReference("systemuser", new Guid("F97371A0-E669-45C7-B611-267E7F2B7E9F"));

SetBusinessSystemUserResponse resp = (SetBusinessSystemUserResponse)service.Execute(req);

If you need help instantiating a service object in .NET within a plugin check out this post:
http://mileyja.blogspot.com/2011/04/instantiating-service-object-within.html

Now here is the Jscript nicely formatted by the CRM 2011 SOAP formatter. Available at: http://crm2011soap.codeplex.com/

Now in BLOCKED SCRIPT

if (typeof (SDK) == "undefined")
   { SDK = { __namespace: true }; }
       //This will establish a more unique namespace for functions in this library. This will reduce the 
       // potential for functions to be overwritten due to a duplicate name when the library is loaded.
       SDK.SAMPLES = {
           _getServerUrl: function () {
               ///<summary>
               /// Returns the URL for the SOAP endpoint using the context information available in the form
               /// or HTML Web resource.
               ///</summary>
               var OrgServicePath = "/XRMServices/2011/Organization.svc/web";
               var serverUrl = "";
               if (typeof GetGlobalContext == "function") {
                   var context = GetGlobalContext();
                   serverUrl = context.getServerUrl();
               }
               else {
                   if (typeof Xrm.Page.context == "object") {
                         serverUrl = Xrm.Page.context.getServerUrl();
                   }
                   else
                   { throw new Error("Unable to access the server URL"); }
                   }
                  if (serverUrl.match(/\/$/)) {
                       serverUrl = serverUrl.substring(0, serverUrl.length - 1);
                   } 
                   return serverUrl + OrgServicePath;
               }, 
           SetBusinessSystemUserRequest: function () {
               var requestMain = ""
               requestMain += "<s:Envelope xmlns:s=\"http://schemas.xmlsoap.org/soap/envelope/\">";
               requestMain += "  <s:Body>";
               requestMain += "    <Execute xmlns=\"http://schemas.microsoft.com/xrm/2011/Contracts/Services\" xmlns:i=\"http://www.w3.org/2001/XMLSchema-instance\">";
               requestMain += "      <request i:type=\"b:SetBusinessSystemUserRequest\" xmlns:a=\"http://schemas.microsoft.com/xrm/2011/Contracts\" xmlns:b=\"http://schemas.microsoft.com/crm/2011/Contracts\">";
               requestMain += "        <a:Parameters xmlns:c=\"http://schemas.datacontract.org/2004/07/System.Collections.Generic\">";
               requestMain += "          <a:KeyValuePairOfstringanyType>";
               requestMain += "            <c:key>UserId</c:key>";
               requestMain += "            <c:value i:type=\"d:guid\" xmlns:d=\"http://schemas.microsoft.com/2003/10/Serialization/\">e497532f-d37c-e011-8d72-1cc1dee8ea49</c:value>";
               requestMain += "          </a:KeyValuePairOfstringanyType>";
               requestMain += "          <a:KeyValuePairOfstringanyType>";
               requestMain += "            <c:key>BusinessId</c:key>";
               requestMain += "            <c:value i:type=\"d:guid\" xmlns:d=\"http://schemas.microsoft.com/2003/10/Serialization/\">9225a2e5-4970-e011-8d78-1cc1dee8da78</c:value>";
               requestMain += "          </a:KeyValuePairOfstringanyType>";
               requestMain += "          <a:KeyValuePairOfstringanyType>";
               requestMain += "            <c:key>ReassignPrincipal</c:key>";
               requestMain += "            <c:value i:type=\"a:EntityReference\">";
               requestMain += "              <a:Id>f97371a0-e669-45c7-b611-267e7f2b7e9f</a:Id>";
               requestMain += "              <a:LogicalName>systemuser</a:LogicalName>";
               requestMain += "              <a:Name i:nil=\"true\" />";
               requestMain += "            </c:value>";
               requestMain += "          </a:KeyValuePairOfstringanyType>";
               requestMain += "        </a:Parameters>";
               requestMain += "        <a:RequestId i:nil=\"true\" />";
               requestMain += "        <a:RequestName>SetBusinessSystemUser</a:RequestName>";
               requestMain += "      </request>";
               requestMain += "    </Execute>";
               requestMain += "  </s:Body>";
               requestMain += "</s:Envelope>";
               var req = new XMLHttpRequest();
               req.open("POST", SDK.SAMPLES._getServerUrl(), true)
               // Responses will return XML. It isn't possible to return JSON.
               req.setRequestHeader("Accept", "application/xml, text/xml, */*");
               req.setRequestHeader("Content-Type", "text/xml; charset=utf-8");
               req.setRequestHeader("SOAPAction", "http://schemas.microsoft.com/xrm/2011/Contracts/Services/IOrganizationService/Execute");
               var successCallback = null;
               var errorCallback = null;
               req.onreadystatechange = function () { SDK.SAMPLES.SetBusinessSystemUserResponse(req, successCallback, errorCallback); };
               req.send(requestMain);
           },
       SetBusinessSystemUserResponse: function (req, successCallback, errorCallback) {
               ///<summary>
               /// Recieves the assign response
               ///</summary>
               ///<param name="req" Type="XMLHttpRequest">
               /// The XMLHttpRequest response
               ///</param>
               ///<param name="successCallback" Type="Function">
               /// The function to perform when an successfult response is returned.
               /// For this message no data is returned so a success callback is not really necessary.
               ///</param>
               ///<param name="errorCallback" Type="Function">
               /// The function to perform when an error is returned.
               /// This function accepts a JScript error returned by the _getError function
               ///</param>
               if (req.readyState == 4) {
               if (req.status == 200) {
               if (successCallback != null)
               { successCallback(); }
               }
               else {
                   errorCallback(SDK.SAMPLES._getError(req.responseXML));
               }
           }
       },
       _getError: function (faultXml) {
           ///<summary>
           /// Parses the WCF fault returned in the event of an error.
           ///</summary>
           ///<param name="faultXml" Type="XML">
           /// The responseXML property of the XMLHttpRequest response.
           ///</param>
           var errorMessage = "Unknown Error (Unable to parse the fault)";
           if (typeof faultXml == "object") {
               try {
                   var bodyNode = faultXml.firstChild.firstChild;
                   //Retrieve the fault node
                   for (var i = 0; i < bodyNode.childNodes.length; i++) {
                       var node = bodyNode.childNodes[i];
                       //NOTE: This comparison does not handle the case where the XML namespace changes
                       if ("s:Fault" == node.nodeName) {
                       for (var j = 0; j < node.childNodes.length; j++) {
                           var faultStringNode = node.childNodes[j];
                           if ("faultstring" == faultStringNode.nodeName) {
                               errorMessage = faultStringNode.text;
                               break;
                           }
                       }
                       break;
                   }
               }
           }
           catch (e) { };
        }
        return new Error(errorMessage);
     },
 __namespace: true
};




To understand how to parse the response please review my post on using the DOM parser.
Now you can call the SDK.SAMPLES.SetBusinessSystemUserRequest function from your form jscript handler.
Thats all there is to it!

I hope this helps!