My impression is that he accepts both fiat and Bitcoin already but is looking for a better payment solution, hence my question above. Hard to suggest the better option without knowing his previous setup though.
if you check the website and try to pay for an order the only payment option are cards, mobile payments and ViaBill. no crypto payment.
You can use BTCPayserver, it's an open-source, self-hosted payment processor that offers a solution for e-commerce platforms, so you don't depend on any 3rd party provider, and you can accept crypto payments without a hassle.
this is also my recommendation for a wordpress webshop.
it's also well documented, so it's easy to set up:
https://docs.btcpayserver.org/WooCommerce/