The Church of the Holy Spirit is located in the Greek Orthodox Patriarchate school building. The school is located on Har Tsiyon St, near Zion Gate of the Old City of Jerusalem.
The Church is only open by appointment or if there is a scheduled Divine Liturgy (which is very rare. Typically only on the Church Feast Day).
Click photo to see larger image and longer description:
HOLY SPIRIT CHURCH- JERUSALEM
On the left hand side is a casket where the Holy Relics of St Filoumenos once rested