1) There is a Mitzvah in its own right to carry the coffin even though the actual burial is a long time later. The source that there is a Mitzvah to carry the coffin is the first Mishnah in the third chapter of Maseches Berachos (17b), which tells us that the people carrying the coffin are exempt from Keri'as Shema if the coffin has not yet reached them. The Mishnah there says that the carriers of the coffin are exchanged several times because everyone desires the merit of carrying the coffin. So even though they do not actually bury the deceased, they still do a Mitzvah by carrying him.

2) Rashi (Berachos 17b, in the Mishnah, DH Mi) writes that the reason why one is exempt from Shema is because his thoughts are preoccuopied with the burial. According to this reasoning, the person carrying the coffin is also exempt from other Mitzvos because one cannot do the burial unless one fist carries the coffin.

3) Tosfos (Berachos 17b, DH Patur) writes that the reason why he is exempt is that the Yerushalmi says that one is only obligated to do Mitzvos on days that he is occupied with living people, but not on days that he is occupied with the deceased. Again, according to Tosfos, the carriers of the coffin were exempt from other Mitzvos because they were busy with the body of Yosef.

4) Therefore the entire activity of the funeral process is considered a Mitzvah and it follows that carrying the coffin is a Mitzvah even though the burial is a long time later.

(You wrote that the Mitzvah was many days later, but in fact the burial was 40 years later.)

Kol Tuv,

Dovid Bloom