Does the letter fa in "falyalbath" denote order and sequence, such that the meaning of the hadith is that Jesus (peace be upon him) will stay on Earth for an additional forty years after his descent?

The aforementioned Hadith (definition) was narrated by Al-Hakim from Abu Hurayrah (may Allah be pleased with him) with the wording: "Indeed, the Spirit of Allah, Jesus, son of Mary, will descend among you. When you see him, recognize him: a man of medium stature, inclining towards reddish-white, wearing two garments dyed with safflower. His head will appear as if dripping, even if no wetness has touched it. He will break the cross, kill the swine, abolish the jizyah, and invite people to Islam. During his time, Allah will destroy the Antichrist (Al-Masih Ad-Dajjal), and security will prevail among the people of the earth, so much so that lions will graze with camels, leopards with cattle, and wolves with sheep. Children will play with snakes without them harming them. He will remain for forty years, then he will die, and the Muslims will pray over him."

His statement: "He will remain for forty years" means that he will stay this period with the Muslims, and there is no mention of his previous period with his people. Other narrations come in sequence with "then," such as the saying of the Prophet (peace and blessings be upon him): "Then Jesus (peace be upon him) will descend and kill him [the Dajjal], then Jesus (peace be upon him) will remain on earth for forty years as a just leader and an equitable ruler."