Redeeming Fortnite PS5 code.

Forgive my ignorance. I’m a gamer but I do not play Fortnite.

So I purchased the PS5. My kiddo loves and plays fortnite on switch and Xbox. My understanding is regardless of platform you have an epic account to log into that you play on.

I assume the same goes with the PS5. I bought the Cobolt bundle and it came with a PS5 redemption code. I assume I would need to download Fortnite on my PlayStation and my son could log into Fortnite while on my PSN profile to redeem the code then logging into his epic account in game to get the content.

Then when he plays on the Xbox or switch he’ll have that content. Correct?