My client wants me to do something specific and I'm sure how or if it's even possible.
Right now, members can purchase a membership on our site and pay for it via PayPal. My client would like the payments to go through Shopify instead of PayPal. I assume that I would need to somehow tell Shopify which product is being purchased and then get feedback from Shopify that the purchase was successful. Is what I need to do possible?
From what you have written, it seems like your site is currently not built on Shopify, in which case I would think you would be better off sending payment through something like Stripe (which is what Shopify payment is based upon).
The request might be broader, where your client might be asking you to move the store to Shopify (again, assuming you are not on Shopify at the moment)
Hope that helps