If he really only wants to run one website/shop where both have the same opening times, menus , prices – i.e absolutely *everything* is the same – you could do it with this
https://support.wp-pizza.com/downloads/wppizza-delivery-by-postcode/
post/zipcodes can be arbitrary in that plugin, so you do not have to say zip1, zip2 zip3 in the plugin, but shopA, shopB etc will also work and you can set the email as required
however, generally speaking – although not my business – you will probably find that one day your client says “oh, I want to close Shop-B 15 earlier” or “‘pizza napoli’ doesn’t sell in Shop-A, let’s take it off the menu” or any other random thing that is different between Shop-A and Shop-B.
At that point you will need 2 websites anyway (although they could of course be in a wordpress multisite setup)
just trying to save you some future headaches, but it’s up to you/him of course…