If it's a business asset you pay for it out of the business account, and get an invoice / receipt made out to the company / business name.
I'm not sure about the "in full" part of your question, because whilst you pay for the asset in full through the business, you then have an asset on your balance sheet which you depreciate (i.e. "write off") over a number of years.
Maybe you're asking if you can claim the amount paid as an expense - in which case the answer is no - you have an asset, which gives rise to depreciation for accounting purposes, and capital allowances for tax purposes.