If you want the migrated mapping to use the same object path as in the earlier environment, you must maintain the same database, schema, and table in the Snowflake account for both the earlier and the new environment.
For example, if you have two different accounts, Account1 used for Organization 1 and Account2 used for Organization 2, the object path for the database, schema, and table name must be the same in both the accounts:
Account1: DB1/SCHEMA1/TABLE1
Account2: DB1/SCHEMA1/TABLE1
You do not need to override the database, schema, role, and table in the advanced properties. If the role used in the connection has access to TABLE1, the mapping runs successfully.