Even Jesus would not have the power to grant everlasting life to anyone—without His death for our sins and resurrection. CS
Sorry, it gets a bit more complicated. It could in fact be that false prophets earlier in their life believed the Gospel for a moment and were eternally saved.
It is also true that those who listen to a false prophet, even though the false prophet has a false message, may be saved.
It may be that the false prophet presents a Bible verse such as John 6:47 or First Corinthians 15:1-4, and in that moment, hearers are saved, so the reality is a bit more complicated than simply saying these are damned people preaching to damned people.
The Bible is very clear that some people who are not believers preach the gospel for money and get people saved.
What we are saying is that false prophets are preaching a false gospel and if that gospel is believed, it does not have the power to save people.
If you get the Gospel wrong, and preach it to others, you are a False Teacher.
Everyone has faults and mistakes and misunderstandings and things they are growing in in their teaching.
Being wrong about many things does not make a person a False Teacher.
False Teachers prevent the eternal salvation of others through their false teaching, by teaching a False Gospel.
Paul the apostle damns False Teachers to Hell, twice, in Galatians chapter one.
The only true Gospel is found in 1st Corinthians 15:1-4.