SQL Server Partial Only Database Move
If the objects you want to move are part of a separate filegroup, then you can do a filegroup backup and restore. This is a little tricky - with SQL Server, you can do a piecemeal restore of the primary filegroup, plus other filegroups, and the objects are then online. However, this won't work if the database wasn't designed for this from the start (by separating objects into filegroups.)

If the objects are relatively small, and if all objects are in a filegroup other than the primary, AND if you were allowed to make changes to the database, then you could create a new filegroup, move the objects into it, and then restore just that filegroup. However, you still have to restore the primary filegroup first, so this only works if there's not much in the primary filegroup.

If those aren't the case, you could set up a new database in the other company's data center, and copy the objects in that you'd like to transfer over. You could do this with simple insert statements, or by setting up replication into the new database.

None of what I've said above is easy - but hopefully it plants a few seeds on other ways you could pull it off.