Texture files are saving locally on individual user’s computer.
When another team member opens the TM project on a different computer, the dialog box ‘Missing Files’ pops up listing all missing textures and an option to select a new path (screenshot below).
The best way to do this is use the Resource Collector (Edit menu > Resource Collector). This will create a folder containing your .TM file and a "maps" folder containing all material maps in your scene, which can then be easily shared between computers.
