Basically FAA STC's do not have EASA approval.
(This is a separate route, expensive and is the usual BS!!
EASA have to reinvent the wheel!
I have STC's that have FAA applicablitly to one model aircraft and the EASA STC referes to other models.
I have also an FAA STC that requires an AFM ammendment and an EASA for the same equipment ( EPGWS by the same company!) that does not.
However that said there is a "grandfather" clause ( as opposed to Santa
If you have an STC that was incorporated on an EU registered aircraft prior to EASA then it is automatic EASA approval.