If the system was already converted, is there an r134a retrofit sticker somewhere under the hood or on maybe a door jamb. The sticker is supposed to be added upon conversion. If you can find it, it will tell you what kind of oil and how much was used. It should have ester type oil in any 12 to 134 conversion.
If this was not done, or if you cannot verify that it was done, the system, at a minimum, should be bled, oil poured out of compressor if you can get any out, and add about six ounces of ester oil. The system should then be evacuated and recharged.
The mineral oil used with R12 will not work well with 134 and can knock out the compressor.
For the other car, the same minimum procedure should be followed to convert. To convert the fittings you can get a set of fittings almost anywhere, but don't use one of the "kits" with suicide hose, fittings and refrigerant. It sounds like you have a set of r134 manifold guages, if you don't that's what you need.
A complete changeover procedure would involve, bleeding, disconnecting everything and flushing, replacing filter-drier, replacing with ester oil, evacuation and recharge.
R134 is much more susceptible to the development of acid if moisture is not completely removed before charging. Pumping down the system with the car in the heat for 24 hours would not be overkill. If any moisture is left in the system, it can combine with the refrigerant to produce an acid which can corrode the system from the inside out.