It is important to get another developer to check the migration for issues.
They should follow these steps:
Start Visual Studio 2013
Open Team Explorer and connect to the new TFS Server
Confirm that they can:
Source Code - Browse the projects and code using the Source Code Explorer
Source Code Operations - Get Latest on a file, make a change and check in
Source Code History - View the history of a number of files in different projects
Work Items - Browse and view recent work items
Open Visual Studio 2015 and repeat steps 1 to 3.
Test that your builds complete successfully on the upgraded build controller(s) and agent(s).
Check that they can create a new Team Project in Visual Studio 2015