Good that that UTI is being treated. They can be difficult to get rid of so go back to the vet after the antibiotic is finished for a re check!
The vet scared me at Max's last senior check up. There were oxalate crystals in his urine. Turns out stale urine will precipitate out crystals. When I had the vet spin fresh urine in house there were no crystals. When Sassy had a UTI the urine went alkaline and the phosphate crystals precipated out. Her crystals were gone once the infection was gone and the urine's pH had reached a more normal level.
Make sure he gets plenty to drink and many chances to empty his bladder.
Here is an article on urinary crystals.
http://www.b-naturals.com/newsletter...ones-crystals/
It is possible the oxalate crystals will stick around. Many dogs do have a problem with them. In that case a special food is needed. A low oxalate food. The special kibble from the vet is designed to solve all sorts of crystals, a tall order and isn't likely to be the reason crystals cease to be a problem. Curing the infection, lots of water and have the urine spun in house so it isn't stale are more likely to help.