Offline Access Client error

A customer came with the following error:

When User X isn't connected to the network, but has synced with OA Client in the past, it's able to show the items.

But when you have a large mailbox, in the bottom you can see the Outlook text: 'There are more items on the server'. This means these items are not in the (local) Outlook Cache?

When the user tries to open these stubs, he receives an error that the server cannot be found (because there's no internet connection)

How can we resolve this?