For God sent not his Son into the world to condemn the world; but that the world through him might be saved.
-John 3:17, KJV
Jesus is the only One who is able to save someone spiritually.
How well or poorly we respond to discovering infidelity ought never to be construed as causing the cheater to get “saved” or be “damned.”
We are not that powerful.
Also, we are not responsible for the actions or lack of action of our cheater. This includes a cheater’s choice to reject repentance and thereby reject God’s free offer of salvation.
The cheaters’ actions are theirs alone to defend before God (see 2 Corinthians 5:10).
Any Christian telling you otherwise is selling a lie. We do not save anyone. That is God’s job, not ours.
(And I would add salvation can only come with repentance or it is not salvation from God–see post here. If the Christian was truly interested in the cheater’s salvation, they would put their effort into encouraging them towards repentance).