You mention backup but do you actually mean copy the partitioned table from one database to another?
There is no object-level backup/restore in SQL Server. A normal backup includes the entire database and a restore includes all objects. Specialized filegroup/file backups can be leveraged to reduce recovery time but the key point is backups are essentially storage-level operations used to restore an entire database as part of a recovery plan, not to selectively copy objects from one database to another.
There a number of options to make an copy of a table, partitioned or not. The appropriate one depends on how how you plan to use the backup copy. For example, if your goal is to have a backup copy of the data in another database on the same instance to recover from a problem ETL process, you could simply use SELECT...INTO
, which will be minimally logged when the target db is in the SIMPLE recovery model. There's no need to bother with partitioning the backup table in that case.