Oh gosh, I assumed MMR was a typo or a (not so) smartphone correction. Thanks for setting me straight. Since MMR vaccines are usually given as a childhood vaccination, I found this information regarding childhood liver transplant.
- Vaccinations Post-Liver Transplant https://www.chp.edu/our-services/transplant/liver/recovery/life-after/vaccinations
It states "The MMR vaccine is given to children, and transplant recipients do not need to avoid persons vaccinated with MMR."

Having said that, I understand your concern and commend you on your precaution. I think this is a question best answered by your husband's transplant team. Are you or is he able to contact a transplant coordinator through the patient portal or by phone?