The permissions on the files and folders will remain when you migrate the data, the share permissions have to be configured using the RBAC roles.
We have introduced three Azure built-in roles for granting share-level permissions to users:
Storage File Data SMB Share Reader allows read access in Azure Storage file shares over SMB.
Storage File Data SMB Share Contributor allows read, write, and delete access in Azure Storage file shares over SMB.
Storage File Data SMB Share Elevated Contributor allows read, write, delete and modify NTFS permissions in Azure Storage file shares over SMB.
To migrate the permissions on the files and folders, you need to use a tool like Azure File Sync, AzCopy or Robocopy
-----------
Please don’t forget to "Accept the answer" and “up-vote” wherever the information provided helps you, this can be beneficial to other community members.