What is the ruling on one who enters the Friday prayer late and does not catch the sermon, but only catches the two rak'ahs?

Question:
I entered the mosque on Friday late, and I did not catch the sermon, but I caught the two rak'ahs, and I added two rak'ahs, meaning I prayed four rak'ahs of Zuhr. Is my action valid?

Answer:
If you are traveling, if you are traveling, then you pray two rak'ahs shortened. You intend Zuhr and pray two rak'ahs shortened, considering it to be Zuhr shortened. But if you are a resident in Makkah or you are not traveling, and you arrive after the imam has raised his head from the second rak'ah, after the imam has raised his head from the second rak'ah, then you intend Zuhr and enter with the imam. When he concludes the prayer, you stand up and you come to the prayer of Zuhr for four rak'ahs?
As for if you catch the imam in the second rak'ah before he raises his head from the second rak'ah, you enter with him with the intention of Jumu'ah. When the imam concludes the prayer, you stand up and you come with one rak'ah to complete the Jumu'ah prayer. Yes.