On one hand, this is a fairly simple fix. On the other hand, the reports dictionaries are sensitive creatures, and should be handled with care. You may want to have your GP partner take a look at your workstation and the other person's, to determine the best course of action.
If you'd like to do some troubleshooting on your own, read on. Before following any steps in this post, please make copies of the pre-existing REPORTS.DIC files that may be overwritten. I would also make copies of the DYNAMICS.SET files, just in case. These will serve as backups, should the need for them arise.
It sounds like their DYNAMICS.SET file is pointing to a different reports dictionary than yours. You may just need to follow these instructions for setting your system up so that all users share a reports dictionary: support.microsoft.com/.../858327
It is usually recommended that everyone use the same reports dictionary, stored in a shared network location. This facilitates everyone having the same version of reports, and makes it easier to update reports. There are situations where individual, local reports dictionaries are a better choice.
If the two workstations are using different dictionaries, the choices are: import the modified report into the other person's dictionary, or change their path to match your path. If the dictionaries are separate for a specific reason, the safer choice may be to import your modified form into their dictionary.
To export the report from your workstation, go to Microsoft Dynamics GP >> Tools >> Customize >> Customization Maintenance. Locate the 1099 form in this list, highlight it, and then click Export. Save the package file somewhere accessible from the other workstation and then use the same window to import it on the other workstation. Here are general instructions on recreating a reports dictionary. These can be useful for some detailed information on how to import/export package files: support.microsoft.com/.../850465
You'll also need to verify that everyone's Alternate/Modified Forms & Reports ID is set to use the modified version of the form. Usually, there is only one ID, but sometimes there are more. Here are instructions for making sure a user has access to a modified report: support.microsoft.com/.../942507
This is a lengthy post - sorry about that! I hope it helps, and if you have questions, post back.