The best practice for working with members of a remote team is to set up the structure for a project on a dedicated drive of a central network server. If you must mirror a server drive, communicate the location to remote teams so they can assign the same drive letter. When remote locations use the same mapped drive, the extended team can work on the project without being prompted to repath the project when it is set current.
If you want to specify mapped drives for an existing project, organize the full project on the specific drive first. Then use Project Browser to browse for the project using the mapped drive letter.