**Short Answer:** It disintegrates.
**Background:** Although I was unable to find any primary reference, there were many secondary references stating that the pollen tube does disintegrate. In very short, after the pollen tube reaches the female gametophyte, the pollen tube nucleus disintegrates. For the 'why', it disintegrates to let the two sperm cells pass through, and also since its function of controlling the growth of pollen tube has finished.
