Two separate things control this, and they fail differently.
The workflow. An order belongs to a workflow. A partner only sees orders in workflows they are
set up for. If a forwarder has access to one workflow and the order sits in another, the order will
not appear in their Action Center at all, even though everything else is correct.
The partner record. The partner on the order has to be the same entity that has users. Adding a
partner under an abbreviation or a similar-but-different name creates a separate entity, and the
users on the real one see nothing.
What to do: check which workflow the order is in, and check that the partner named on the order
is the entity your contacts actually log in to. If a forwarder should see more than one workflow,
that can be arranged.
Example
A forwarder has access to a workflow, but the order sits in another, so it never appears in their Action Center. Separately, the order lists a partner under an abbreviation, creating a separate entity from the one the forwarder’s users log in to, so those users see nothing. Checking the workflow and the exact partner entity resolves it.