Hi,
According to your description, I understand that want to deploy DAG in your environment, and want to know how to move Database to DAG members.
Also, I want to double confirm the environment topology:
Original environment:
One Exchange server with MBX role
One Exchange server with CAS role
After change:
Two Exchange server with MBX role
Two Exchange server with CAS role
If I misunderstand your concern, please do not hesitate to let me know.
What are you meaning of in another environment setup in thread subject? Are you want to build an separate Exchange server in another AD forest?
We can use database portability to move a Microsoft Exchange Server 2013 mailbox database between Exchange 2013 Mailbox servers in the same organization. For your reference:
https://technet.microsoft.com/en-us/library/dd876926%28v=exchg.150%29.aspx?f=255&MSPPError=-2147217396
If you want to move mailbox database across forest, we may be need to deploy mailbox move for across forest. Please refer to:
https://technet.microsoft.com/en-us/library/ee633491(v=exchg.150).aspx
Thanks