Sorry to be pedantic but there is no FD on the B737 HUD.
There is a guidance cue, which gives FD information. In AIII mode it gives similar information to the FD but this information is not coming from the aircraft FD computer. But even this is not used for the landing.
For the landing, there is a flare guidance symbol which rises from below once below flare height (AIII mode only). Once the flare guidance symbol reaches the flight path vector, the flight path vector is raised to follow it by pitching up (flaring). This is not the only information available for the flare - there is also the relationship between the HUD horizon line and the flight path vector (which effectively gives a rate of descent in the flare), and a radio altitude within your field of vision. There is also a runway graphic that appears to assist with lateral position. It is possible to land very accurately in zero visibility with all this information. I just wish my country's regulator would hurry up and approve it's use!