I have a 2004 f150 and had the alternator rebuilt
replaced my battery. the red battery warning light is on and I am getting a P0622 code

 

https://www.autocodes.com/p0622_ford.html

Detailed troubleshooting steps:

https://www.obd-codes.com/p0622

 

What was the problem that triggered the rebuild?
The rebuild job may be the issue now.
The PCM controls charge with a signal to the regulator..
That control may have been ignored on the rebuild.
Your shop should know this and be able to test the control function.
The 622 code describes the fault with this function.
Good luck.