Applying expense in this FY to next FY

If you follow GAAP accrual-basis accounting, when you receive money for work not yet completed, you have Deferred revenue (also called Unearned revenue, which means customer paid in advance).

For this, debit Cash (asset) account on date you received the money. (QB account "Bank"). Credit side of entry must go to liability account called Deferred revenue (=Unearned/Customer advance).

That amount is a liability since you owe it back to customer until you complete the work as paid. As you earn revenue, move amounts from unearned to earned revenue. May be all at once or in pieces.