Parallels tools shared clipboard: Set the PRIMARY selection

It seems that the shared clipboard integration exclusively replicates only the CLIPBOARD selection.
I find this difficult to work with, as it makes the use of the PRIMARY selection inconsistent.
Is there a way to tell parallels tools to sync the PRIMARY selection to the MacOS pasteboard and vice-versa? Ideally it would attempt to work both with the PRIMARY and CLIPBOARD selections as other tools do, but I realise that's a difficult problem.