If the front mechanism is moving back to the inner by itself, the stop screw can't be at fault.
The front mech is spring loaded to return to the inner ring, but the clutch mechanism in the lever should hold the cable to stop it doing so.
So my thought would be there is something in the lever that is not quite right. Could be broken or stuck. If the latter, a good squirt of wd40 might help.
The cable should be tight when on the inner ring, but as you can move the FD to the big ring , it can't be that slack.
Is it a new cable? Could it be that it wasn't routed correctly?
Hope you fix it - good luck.