You cannot convert an ICAO FI Certificate to an EASA FI Certificate however; you can obtain credits for your experience as detailed in CAP 804 Section 1 Part Q Subpart 2 Para 1.6
1.6 ICAO Flight Instructor Rating (A) or (H) holder to Part-FCL FI (A) or (H) Certificate
1.6.1 Complete a course of at least 30 hours of ground instruction at an ATO
1.6.2 Complete a minimum of 15 hours Flight Instruction including a recommendation for test at an ATO
1.6.3 Pass the Part-FCL FI(A) or (H) Assessment of Competence appropriate to the aircraft category.
As the conversion is based upon experience there is no need for the ICAO certificate to be current.
You will need at least an EASA PPL and have demonstrated EASA CPL level knowledge (Not necessary to teach for LAPL).
The FAA CFI certificate may be useful for conducting BFRs