Hi Hanobaby
In principle, the answer would be no, B would not have to charge VAT to A if A imports the goods.
UK VAT is chargeable either on a supply of goods or services made in the UK. It’s also chargeable on imports of goods and certain services into the UK.
So you have to establish whether a supply of goods is made in the UK. See section 4.8 of VAT Notice 700 which explains the place of supply rules. http://tinyurl.com/6g5884w
A supply of goods is made in the UK if the goods are physically located in the UK when they are supplied. A supply is regarded as made outside the UK if the goods are physically located outside the UK when the goods are supplied. In that case, UK is only due if and when the goods are imported into the UK.
So in the situation you describe, B would not charge VAT to A, but A would pay import VAT when the goods arrive in the UK from China. A can reclaim the import VAT on its VAT return under the normal rules as set out in VAT Notice 702: Imports.
Marie