As you knew, Customer Groups in EShop are used to divide customers of your store into groups for the discount price or tax calculation purposes. Normally, store admin must manually edit customers and assign them to specific customer group. However, since version 1.2.10, EShop has a feature to integrate with Membership Pro extension to assign customer to a specific customer group automatically after purchasing subscription from Membership Pro.
If you are using previous version of EShop, then simply update it to latest version. If you don't want to update EShop, then just need to choose plg_osmembership_eshop.zip in the package to install it as a normal plugin in Joomla. If you are installing a fresh latest version of EShop, then it has already had the integration feature.
First, you should go to Extensions -> Plugin Manager to filter Membership Pro - Eshop Plugin and enable it. Then, go to Components -> Membership Pro -> Subscritpion Plans. When you edit a plan, you will see a new tab called "Eshop customer groups settings". Under this tab, you will see a list of Customer Groups in EShop, let choose a customer group and Save. Now, when users buy a subscription in Membership Pro, they will become a customer in EShop and they will be assigned to corresponding Customer Group which is assigned to the subscription plan.
EShop has a tool to migrate subscribers from Membership Pro into customers in EShop. Go to EShop -> System -> Tools, then click on Membership button, the system will do the migration automatically and show you the successful message once it is done.