The question doesn't make an awful lot of sense presuming that the partnership has had accounts made up each year (or if it's shorter than a year, it's getting accounts done for the period).
All partners have a capital account which will have in it any monies they invested in the business, add any profits it made, less any losses it made, less any drawings they took. The net bottom line is what each partner is due (unless they agreed something different). If person A invested £20k and person B nothing at all then Person A's capital account is £20k and person B's in Nil. The assets of the partnership will be sold off presumably and applied to the capital position. Profits or losses would be presumed to be 50/50 in the absence of any agreement, written or implicit, to the contrary.
Can't help but feel this is being made out to be far more difficult than it actually is?