You're not getting it mate. If you buy a player for an amount of money then you accrue it in the accounts REGARDLESS of the payment terms.
But this is not about FFP.
Let me put it as simply as I can. LFC will be forecasting that revenue will increase year on year, especially as they are expanding the stadium. If we give them £40m cash then that would enable them to buy their own £60m player and pay over 3 instalments over 6 years. But they'll still have £20m of our cash in the bank to buy another £60m player on the same basis. They know with better tv money and match day income they can fund the second two payments, so we've enabled them to buy the players.
Another way to look at it is that they need to borrow £200m to develop a stadium. To borrow that cash will cost them £300m over ten years. Now, they need to borrow less so the loan of £160m will cost them £250m over ten years. We've saved them £10m by paying upfront.
Of course I'm simplifying it hugely, but cash upfront is more valuable than cash 'on tick' because of interest rates. I'm not even touching on the interest you can gain by having that cash in the bank.