Cement port closure sleeve for a subsea well

A subsea well assembly has a cement port closure sleeve which opens and closes a cement port in an outer wellhead housing. The outer wellhead housing secures to conductor pipe. An inner wellhead housing is lowered into the outer wellhead housing before the well is drilled past the conductor pipe, and without having any casing secured to the inner wellhead housing. The sleeve opens and closes an inner return port that extends through the inner wellhead housing and which registers with the outer return port once the inner wellhead housing is in place. Drilling through the inner wellhead housing takes place with the sleeve closed. Subsequently, when casing is run, the casing hanger will engage the sleeve and move it to an open position. This allows cement returns to flow out the inner and outer return ports.