Wow, your kiddo's shot schedule was totally messed up. I'm so sorry for that

.
First, they shouldn't have even given the one at 7 weeks old, it's useless.
Second, they should've waited 3 wks between the series...meaning, if they gave the series at 9 wks, the next one should've been 12 wks, the
last one would then be 15 weeks and he would've been done then - except for rabies.
Now, you're stuck w/ the last one given at 13 weeks, which is controversial and really stinks bc, really, the last shot series should be scheduled to be done btwn 14-16 wks old bc of the maturity of the immune system.
Also, I'd never give a 9-way as I don't allow them to give lepto vaccines to my kiddos.
So if it were me, I'd have your daughter talk to her vet boss as to how they screwed up the schedule. The question would be "Can we end the last series at 13 weeks, or it
absolutely necessary to schedule the last series when the immune system is at least 14 weeks old?" -- that's essentially what you're asking.