Invoicing VAT exempt organisations

[judas]

We have a couple of upcoming project with one of our long-standing clients. The work is ultimately for a VAT exempt educational organisation. Our direct client is also an educational institution but not VAT exempt, nor are they VAT registered (they're a University). What's the situation with charging VAT? I'm thinking we still have to charge VAT even though the work is ultimately for the VAT exempt organisation. I don't think we have the option to directly invoice the end organisation. If we do charge VAT is there any way for a client to recoup this?

Thanks!