Checking in a project using the desktop can be done by navigating to:
File --> Close
A new pop up window will ask you if you want to "Check in" the project.
Make sure you publish the project if you want the new information to be saved and visible to others and reports.
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There isn't a check in button in the tool, because Microsoft assumes you are done with the project at the moment you want to check it in again. If a separate check in button is needed you might need to make a macro.