Is it permissible for a Muslim to openly declare his repentance from a sin he used to commit openly, and to speak about the reasons that helped him repent to his former bad companions, hoping they might be guided, especially if one of these reasons was maintaining prayer and one of them had abandoned it? Is there any element of showing off or openly declaring a sin in this? And does the threat of not being forgiven for openly committing a sin disappear with his repentance?

There is no harm in speaking about repentance and the guidance one has found, especially if it leads to inviting others to emulate them. This is not considered showing off (riya') or publicizing sin, unless the intention is indeed riya'. The blameworthy riya' is seeking status in people's hearts through acts of worship. Displaying good deeds is commendable for someone who is emulated if the intention is to encourage emulation, or to teach and benefit, or to awaken the heedless, such as a righteous imam who is followed. As for the forbidden publicizing of sin, it is reporting past sins boastfully and spreading indecency, whereas mentioning them for a need, such as seeking a fatwa, or speaking of the blessing of guidance, or encouraging repentance, is permissible and good.