All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
First of all, you should know, dear brother, that intention means to resolve to do something. Ibn Qudaamah, may Allaah have mery upon him, wrote in Al-Mughni: “The meaning of intention is to resolve to do something, i.e. to have the resolution in the heart to do something, and to be determined to do it without hesitation.”
Therefore, whoever wants to pray the Friday prayer, he should intend in his heart to pray the Friday prayer; by doing so, he would have made the required intention.
However, he should not intend the Thuhr prayer, because whoever intends the Thuhr prayer instead of the Friday prayer, then this is not sufficient for him instead of intending the Friday prayer. This is because the Friday prayer is the obligatory prayer of its time and it is a separate prayer and not a shortened form of the Thuhr prayer, according to the correct opinion of the scholars.
An-Nawawi said: “The Friday prayer is not valid by merely intending to perform the Thuhr prayer and it is not valid if it is performed with the intention of a shortened Thuhr prayer if we say that it is a separate prayer, but if we say that it is a shortened form of Thuhr, then this is correct.”
Allah knows best.