The controller is the same part number. And I did the matching over. Still no luck

In matching, the load sensor and tilt angle sensor parameters are reset. there is a sequence in the manual to be followed to accomplish this. if they are out of range, the mast will not function correctly when extended beyond the lift height switch. if they cannot be set, then one or more of the sensors may be faulty. when switching controllers, make sure the part number matches as they used more than one controller. when the controller is changed matching has to be done.

It does have that SAS system and it only stops tilting back when it passes the Heights sensor on the first mass. I did a relearn on the mass level. I even tried a module out of another machine. I even tried a used height sensor. I also checked the microswitches at the hydraulic control.

Provided there is no damage to the wiring for the SAS system, try performing matching as described in the SAS/OPS manual supplement available from Toyota. This suppiement alos outlines troubleshooting SAS.

Does this have self leveling tilt with the push button on the tilt lever ****? Also, how about the height sensor switch on the top of the mast channels? I know there is a solenoid on the control valve that can shut off the tilt when SAS kicks in or the self leveler senses forks are level with the button pushed and the sensor on the right tilt cylinder senses the mast is level. Just some ideas, it's a very complicated system.

Mast tilt forward & back are both monitored & controlled by the SAS system.

Do you mean when the mast is FULLY EXTENDED (all the way to the top) or just if the forks are off the ground?
Does it act the same way when the forks are unladen, or only when a load is on them?
The simple approach to this is to ask...Is the hydraulic tank filled to its correct level?
If the hydraulic tank is not filled to its correct level, it is possible that the pump is running out of oil after filling the lift cylinders to the point there is not enough oil left to operate tilt back.
But, if that were the case, the mast is likely not being lifted to its fully extended height at all.
Another possibility is that the truck might have the Toyota SAS system on it. If that is the case, it just got more complicated.
Look on the mast where the large hydraulic hose coming from the truck connects to a squarish shaped valve.......does this valve have a sensor with a wire attached to it?
If there is a wire connecting to a sensor on that valve the truck may possibly have the Toyota SAS system on it.
If so, you may have to have a Toyota tech check out the truck because the Toyota SAS system controls the hydraulic functions of the mast and steering axle under certain conditions.