If I own two businesses am I allowed to purchase something from business A as a promotional it for business B and claim the full value as a write off?
Yes. As Critter 3 explained, Business A reports the sale amount as income and Business B deducts the purchase amount as a business expense, assuming the item was used for a business purpose.
That said, it's not clear what your wording means ("as a promotional it for business B"..... "claim the full value as a write off"). What is the item and how will Business B use it?
I was doing a monthly promotion and giving away a summer swag bag full of summer products for my tea business (Company B). Items included were a custom made beach themed tumbler that was from Company A, tea, and a beach thermal.
The answer is still the same. Company A reports the sale amount as income and Company B deducts the purchase amount as a business expense, since giving away items, to potential customers, as a promotion, is a legitimate business expense.