VAT Involving US Customer

Hello, I have a sale to a customer based in the United States. Normally we export, no VAT is charged, very easy. However, in this instance, their end-customer happens to be in the UK. To save time/freight costs, they want to simply collect the product from me, and deliver to their customer. The issue we now have has to do with the VAT. Normally, their customer would pay this when they import the product, along with any other import fees that may arise. My customer, the US person, can not charge them VAT as they are a US business. The question is- how do we transact this sale? The idea of shipping to a bonded warehouse came up, but Im not sure if that is feasible. Has anyone have a similar experience with this?

Hi.
If the goods are not being exported out of the UK then you are making a UK sale to the US company on which UK VAT would need to be charged.
When the US company makes their supply to their UK customer then this sale would attract VAT and so there would be a requirement for the US company to register for VAT in the UK.
Please see the guidance below:
Non-established taxable persons — basic information