Definitely be good to take him to a vet and get him all checked out. Was his stool previously firm on something else he was being fed? If so, I might be tempted to going back to that food depending upon what it was. Did the boarding facility have any info on his health history and food history?
Bless your big heart for welcoming this precious one into your home
. Poor fella, being abandoned like that...wonder why his owner did that to him
.