AWS Account Migration using DMS (Data Migration Service)

Question

We are planning to a cross account migration using DMS, where we would need to do migration of data from one aws account to another, in which the data from the source account will just be added to the target account. And the data in the target account will not be affected.

After the migration. The data in the target account should look like this:

Target account = data from source account + data in target account

Note: both accounts have existing data

Would someone be able to provide some steps on how to do this?

I tried manually adding the data from source to target, but this may not be a reliable way