I appreciate your work peter but This Script Steps will not work Correctly and will not full fill your requirement as want, As I know GTRR Is used for viewing related records either from your portal or the record which you are seeing in browse mode, But here case is different you are choosing value from drop-down list and after choose user you go for it's related record by using GTRR which is actually not possible.
What Should you do just capture the User-Id of Selected user from That dropdown text box in continue button script and go to "Record Detail - Project_AdminFilter (Project)" in same window which you used for showing pop-up message, and then Enter find mode, and send capture Id/name What ever to the filed In This table and perform Search. after this it will show all record associated with that user.This is the one way you can achieve your requirement.
There is another way by which you can achieve same thing, By use Relation ship Based on global variable, Use a global variable which will capture User Id and and make relation ship with Project and use that Portal in "Record Detail - Project_AdminFilter (Project)".
Why do you have close window as the first step? That puts your in a completely different window where the current record, layout and value in your field where you selected a user may be different.
This script works from any layout, including the projects layout. gSelectedUser must have global storage specified or the script will not work:
Go To layout [projects]
Enter Find Mode  //clear the pause check box
Set field [Projects::UserNameField ; YourTable::gSelectedUser ]
Set Error Capture [on]
If you use a drop down list, the OnObjectExit trigger can perform this script automatically when the user selects a value in the drop down. If you use a radio button or pop up menu format, OnObjectModify may be used for the trigger.