Additional SQL Server features and topics not covered by specific categories
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.