RE: Is Microsoft GP 2013 compatible with Office 365
As an added note, this is what I found in the GP 2013 setup guide:
The following components also must be installed before you can install Microsoft Dynamics GP.
• Microsoft Application Error Reporting 11.0
• Open XML SDK 2.0 for Microsoft Office
• Microsoft Lync 2010 SDK Runtime
.... (among another list of products)
Also, in regards to Word Templates, this is what is required to make it work:
• Visual Studio Tools for Office Runtime 2.0 or later—Visual Studio Tools for
Office Runtime 3.0 is installed with Microsoft Dynamics GP Add-in for
Microsoft Word
As for e-mailing out of GP 2013, those where the restrictions:

