Access Website With Reverse Proxy

I'm hoping to get some kind of idea if what I have in mind is even possible or if I'm looking in the wrong place.

Basically, my company provides a website which users are able to access online with credentials we sell and provide them. We have another potential customer who would like to access this website. Sadly this customer is very stuck in the past, and they don't allow their users any internet access at all.

For a number of reasons, I don't want them to host their own version of this website. However, I considered that we might configure a web proxy on their network (which is given internet access) which reverse forwards connections to our website. Is this even possible? And should it be attempted? Or are there better ways to achieve this?