R134a conversion often requires replacing, o-rings and some times hoses. You will need to flush the oil from the system and recharge to system with an oil that is compatible with R134a.
For a system like yours, you can leave the hoses, oil and o-rings alone and replace the refrigerant with a blend like Hot Shot (trade name). The auto shops like to do the conversion to R-134a so they can make more money. Some shops will try to short cut the proper procedure which usually winds up in a problem.
With the blend, you need to evacuate the system to get all of the R-12 out and then recharge with Hot Shot.
ICOR International, Inc.