Pup is a 7 month old JRT. Had problems with him being a fussy eater (have to top dry with wet food else he doesn't touch it) and also loose stools on every puppy food I've tried him on. Ran out of puppy food yesterday and gave him a bowl of big dogs dry kibble, which he wolfed down with no meat topper, and has eaten for every meal since happily. I'm tempted to keep him on it, as have had no loose stools today at all, and he really seems to like it. I know the recommendations are 12 months, but he's a small breed and the vet reckons he's about fully grown now, so would it be so bad to put him on the same food as big dog?
I don't use puppy food at all. I feed my lot Millie's Wolfheart which is good enough quality to not need a separate puppy formula (more often than not the only difference between puppy and adult food is that in the puppy formula more of the protein comes from animal rather than plant sources) so pups just go straight onto that when they arrive.
Another one that hasn't used puppy food for either of my two (2 years and 1 year). Both have Millie's Wolfheart too, their Facebook page and website are excellent. It's not cheap but doesn't contain grain or rice at all.
Our pup was on Millies Wolfheart from around 6 months, loose stools stopped within a couple of days.
What is your other dog on? If it's a good quality food like Millies you might not need to use a puppy version, if its a food low in quality proteins you should contend with the puppy food or switch both to a better food.