How to check if the user comes from another specific site?

My boss wants me to do a thing on our website and I don't know if it's feasible.

Our website has a shop, and the user can buy items.

Wat my boss wants is the following: if the user comes from a partner site, when he purchases the items, the other site gets a remnueration (like 5% of the order).

I don't even know if this is possible! If it was only one site, it would be easily doable with javascript, sessions and the following.

But checking if the user comes from a whole other site? This seems super hard to do.

Here is a recapitulative drawing of the query:

Situation 1
User ---------> Our shop

Our shop gets 100% of the amount the user paid

And

Situation 2
User -----> Partner store ----> Our shop

Our shop gets 95%, partner shop gets 5%

Also our site is made using prestashop.

Thanks a lot everyone.