Death is a consequence of sin (Romans 6:23), so it is impossible to be immortal and then to sin.
When people are made immortal they will share in God’s ‘divine nature’; 2 Peter 1:4 says:
… he [God] has granted to us his precious and very great promises, so that through them you may become partakers of the divine nature, having escaped from the corruption that is in the world because of sinful desire.
Peter says that corruption — the opposite of being immortal — is the result of ‘sinful desires’. So to escape corruption and become a partaker of God’s divine nature — to be immortal — requires the removal of sinful desires. This means that once people are made immortal they will no longer be able to sin, their sinful desires having been removed. This is such an exciting prospect!