Hello,
the gearbox hold on the 1st gear and when I turn it off and on it shifts normally and after minutes back to the same problem again (H2 6.2 2008 6speed)

 

If you have a GM Tech2 tool you should be able to test the actuation of the solenoid. BTW, when was the last fluid/filter replacement? A clogged up filter that causes low line pressure can cause a bunch of issues for the 6L80.

 

Will test it ,I changed the body valve tcu only

 

My transmission is pretty new and it occasionally does the same thing. Idk what it is. It just throws a fit all of the sudden. It only happens when manually selecting 1 or 2 (the numbers on the shifter not tap up/down on the wheel).
last time it was really bad. I went from 1-2 and when it finally engaged second it chirped all 4 tires.

how many miles are you at? Could be time for a fluid and filter change?

side note: a tin can would have been a better option for the h2 than the 6l

edit: I now see it’s a constant issue for you. Check fluid level, Inspect wiring and do a filter/fluid change and inspection but chances are to put it nicely… you’re f*cked.