When you move inventory to a new Magento server, the product data (e.g. Product and Order identifiers) may be changed. M2E is strictly connected to a Magento server you use, so the data change can impact your M2E Pro settings and listings.
To save all your M2E Pro data and settings while moving to a new server, please follow the next steps:
1) Transfer M2E tables (all tables with names starting with m2epro_ and ess_) and Magento core tables to a new server. For that, you can use Magento backup tool or full MySQL dump.
2) Install the same version of M2E Pro on another Magento site (Magento version should also be the same).
3) Obtain the new license key on https://clients.m2epro.com and set in M2E Pro on new Magento.
For more information, you are welcome to contact our Support Team at firstname.lastname@example.org.