Hi there @frosti_pro , 
So you can have a look at this blog https://www.databricks.com/blog/migrating-tables-hive-metastore-unity-catalog-metastore , helped me a lot when we were doing migrations for a client

There's a tool from databricks called databricks-ucx which is used for migration from hive metastore to UC. 
You can also have a look at it for migrating from external to managed tables will get an idea or step required
https://databrickslabs.github.io/ucx/docs/process/#migrate-hive-metastore-data-objects

Your usecase is different you want to migrated from UC external to managed , so not all the things will be same but you can get an idea on how to plan the procedure for production

Thank you @ashraf1395 for your reply! I am surprised to see there is no official procedure for my usecase. Thank you again.

Please check out our new docs page! This has some information which may help you, including information about our new SET MANAGED command. We are also looking to make this process smoother over time, so if you have any feedback, please let us know. 

https://docs.databricks.com/aws/en/tables/convert-external-managed