If the "save project in the panel" option had been selected when the project was being downloaded, then yes, you can upload it back. Otherwise - no luck; start from scratch.
To make things mor complicated, GP-Pro was not the only software development system for these screens; a lot had been developed using QuickDesigner, which is an entirely different beast (owned by GE now).
Ask your customer if he may spot any clues being displayed when the unit powers up (like firmware name/rev level etc) or if he can take snapshots of some of the screens - sometimes you may guess which software package was used just by looking at the screen objects.