AC problem: Tenant complainted AC doesn't work when highter temp

a new units. The technian found the new condeser using R-410A, but the air handler is for R-22. Technian asked at least $500 for add a conveeter. Question: is it right? If I change R-410A  expension valve (TXV), will it solve the problem. It cost $60 only in e-bay.Thanks for your help!