My primary recommendation would be to keep puppy on the owner’s walking schedule (same times of day and route), and you may have to increase frequency of walks. Normally, with movement,nature takes its course and dog’s will eliminate.
However, this is a puppy, which can be unpredictable. Hopefully, puppy didn’t ingest anything concerning.
If the dog wasn’t outputting feces at all and still was eating, I’d check with the owner if they are okay with you giving a little bit of pure 100% canned pumpkin (very important to Not get pumpkin pie mix which contains spices) to move things along.) If for some reason that’s not workable, ask if the owner would okay plain, steamed, cooled, and diced or ground broccoli. With both of these food additions, it’s advised to gradually give - meaning a 10 lb dog may only need 1 tsp. at a time.
He may be a shy pooper. Try not looking directly at him if he seems ready to eliminate.