Hello Horst,
Thank you for your interest in EasySocial. Yes, we do have a built-in migrator that helps you migrate items from JomSocial over to EasySocial
However, not everything will be migrated yet though because EasySocial does not have Groups and Events yet until version 1.2.0 . However, once the groups and events are available, the migrator would be able to support it.