Hello I,,

You ask, when Peter was really converted and you point to Luke 22 v 32, where Jesus says:
"But I have prayed for you Simon, that your faith may not fail. And when you have turned back; strengthen your brothers".

Conversion is an ongoing process. It begins in your soul and gradually breaks through to the deepest of your inner, your human spirit.
In Luke 22 v 32 Peter was already converted, how else he could have said what he said to Jesus, Matthew 16 v 16:
"You are the Christ, the Son of the living God".

But Peter did not yet know his own weakness and depravity. He was standing for the greater part in his own force.
HE shoul be able to , HE should do it, so he meant, as his answer proved. For that wrongness he should need an eye. He should break with this fault, he should have to converse ( turn back) also from that. And this should happen through the things to occur, (his denying and so on).

And so the story is a warning to us. O sure, we are converted, all of us, but has it gone already to the deepest of our being, our spirit.
And even then.... satan is contstantly on the way to rob our conversion from us. We have to consolidate it in 'being reborn' by reading the bible with an open heart, ( 1 Peter 1 v 23) and being baptized with the Holy Spirit, as you read it for example in Acts 8, 10 and 19.

And even then: be happy and glorious in Jesus and God, the Powerful and the 0ne of splendid beauty. But always be well aware of satan, and fight him, in the name of Jesus, ( James 4 v 7).

Greetings
Ger