Laser Hair Removal and the Beard
Generally speaking with laser hair removal you are damaging the hair follicle to the point that it does not grow anymore. Sometimes after a long period of time the beard hair will start to come back. Using minoxidil most likely will not bring back that hair as you did not lose the hair as a result of DHT hormones. The hair follicle was destroyed by a laser and thus may not recover. If you have patches in your beard, you may look into beard transplantation to fill the patchy areas.
Up to you
If it works for you, then why stop? Then again, have you considered that laser hair removal sometimes isn't permanent?
Beard hair growth
If you are happy with the growth by using minoxidil you can continue using it. The only way you can tell if the beard hair will thinned after stopping minoxidil is to stop and see what happens.
Beard Hair Loss After Laser Treatment
Laser hair removal destroys the follicles of hairs and the hair that is gone should not be able to grow back. I guess the hair growth that you have experiencing must have been the hair that have been in resting phase during the laser treatment time and have not been affected by treatment.
I am not sure Minoxidil can do anything to reverse the hair loss after a laser hair removal treatment. If you have patchy hair loss that is bothering you, hair transplant could be considered to even out the appearance of your beard hair.
Bear problems after hair removal laser
Yes, you can have a hair transplant if the growth with the minoxidil if it not satisfactory with the minoxidil. Alternatievely, you can repeat the hair removal laser process until all of the hair is gone. This fequently takes many sessions