It is a common requirement to be able to move the synchronizer to the new system.
Here we will describe full list of steps required to make successful move.
The Agile SugarCRM to Exchange Synchronizer service should be stopped and disabled to proceed with move:

The service stop process may take up to a few minutes. This is normal and it is recommended to wait until the process ends.
Zip the folder: C:\ProgramData\GrinMark\AESync (or c:\Documents and Settings\All Users\GrinMark\AESync on older systems).
Go to new server and install same instance of AESync from the setup package
Unpack contents of the .zip package into C:\ProgramData\GrinMark\AESync (or c:\Documents and Settings\All Users\GrinMark\AESync on older systems).
Launch the Agile Exchange to SugarCRM synchronizer tool. It should install and run the service.