Mongo Management Studio provides the functionality to copy a collection. Therefor 3 options are available.
Copy a collection within a database
A collection is copied within the same database. Only the name of the destination collection must be entered.
Copy a collection to another database on the same MongoDB server instance
The collection is copied within the same MongoDB server instance to a different database. The name of the collection is maintained and must not already exist in the destination database.
Copy collection in another MongoDB server instance
Copies the collection in any database on the destination server instance of MongoDB. If this database does not exist, it will automatically created. Otherwise applies also here that the collection still may not exist in the destination database.
If an authentication via a userSource is needed for the copy operation on the MongoDB server instance, the field "login database" offers the ability to specify the appropriate database, against which must be authenticated. Otherwise the authentication data can be entered in the connection string for the destination server.
For this functionality is important to note that the naming conventions for MongoDB collections are complied with and the new name does not already exist in the database.