This needs to be moved to the NETBACKUP group.
The only way you will be able to migrate the data is by DUPLICATING it, this will be a slow process.
Both storage providers above would provide their own OST plugin, I would assume the DataDomain plugin is already installed on the backup server, you would need to install the StoreOnce one on there too..
The version of netbackup 7.7.3 is past its EOL and is out of support, I would expect that if you are adding in a NEW HP StoreOnce you will have a NEW OST plugin, it is likely that this will not work with the OLD NBU version.. so you may need to consider upgrading the NBU version before you start.