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 is His slave and Messenger.
If the Imam of the mosque was appointed to deliver the Khutbah (Friday sermon) by the competent authorities like the Islamic Centre or the mosque congregation… etc., then it is unlawful for anybody else to do that mission in his presence without his permission and consent as this might lead to trouble and temptations.
The Prophet said: “No man must lead another in prayer where (the latter) has authority, or sit in his place of honor in his house, without his permission.” [Muslim]
Now, if the appointed Imam permits another Imam to give the Khutbah (the Friday speech) or if the community or the government appoints him to do so, then it becomes lawful for that Imam (who is not the regular Imam) to deliver the Khutbah and lead the people in Jumu'ah prayer. It should be noted here that the majority of Muslim scholars are of the opinion that it is desirable for the Imam who delivers the Khutbah to lead the people in Jumu'ah prayer as well.
Allah knows best.