I have had 3 rescue GSD males all 10 years or more old when I had them & the one who clung most & was mine & had no regard for others was the one who had been chained up outside & had no love till I had him, the two who had come from loving homes actually settled in better.

Most serving police dogs stay with their handler's family when they are retired, but not all. Those who don't are apparently usually happily rehomed elsewhere and police dogs DO definitely form a strong bond with their handler over the years - as it is not encouraged for anyone else to make a fuss of them.

My very first foster was completely devoted to me and was so unbelievably loyal to me. I had her for 8 months before she was adopted. When I first dropped her off at her new home, she was staring at me with a puzzled look on her face as if thinking why I was leaving without her. They said she was trying to follow me when I drove off (thank the stars she was on a leash). She settled in just fine after a short while and became just as devoted to the mom until the day she passed.
My husband has his dog, he had him from before he met. He is his dog and it is obvious. When he goes away, he travels often for work, he sulks around for the first day or so, then perks back up and is my shadow until hubby returns home.
So I would say, most dogs would transition just fine as long as the home is an appropriate one.