Proxy front-end routes to another domain under the same domain

I have a web application which is hosted at www.shop.com and another web application hosted at domain www.products.shop.com.

A user comes on the page www.shop.com and wants to buy a product. All the information regarding the product purchase is hosted at domain www.products.shop.com. Curently i am redirecting users as from www.shop.com to www.products.shop.com?product_id=8789779.

This is a bad user experience.

What i want?

I want to proxy www.shop.com/products to www.products.shop.com, so www.shop.com/products?product_id=8789779 will load the page of www.products.shop.com?product_id=8789779.

In simple terms i want my users to be on the same domain/url in the browser.

Is this possible?