I was using the M2epro module version 6.4.14 in Magento 1. I was asked to upgrade to a special version of the extension 22.214.171.124 which supports M2epro migration from Magento 1 to 2. You can upgrade to version 126.96.36.199 only form the version 6.4.14, so if you are using any other version, first of all, please upgrade to 6.4.14 and then to 188.8.131.52
In Magento, you should have M2E Pro version 1.2.1 installed
The rest of the steps can be followed by the document. Please ensure that if you are using Magento Data Migration Tool, exclude m2epro databases during migration. It took 2-3 hours for the migration process to complete. Additionally, we had a few issues which were solved by the m2epro support team in a period of 2 days.
Once the migration please upgrade the m2epro extension to the latest version. After installing the specified extensions you can also contact the m2epro support team if you want them to do the migration. Hope it helps you.