Receiving the balance you had written down
You had thought you wouldn’t receive the balance in full so you recognized an allowance on the balance sheet. What you had there, was the receivable balance in full and an allowance for the very same receivable. With recognizing the allowance, you also had to bear some expenses in the same amount.

So, in this situation, with those accounting entries made, you now receive the payment from your client. Be it that they found some additional investment and are now to meet all their obligations etc., what you should do now, is the following:

1) Recognize the cash received
Db Cash and cash equivalents
Cr Accounts receivable

2) Get rid off the allowance made because the receivable it was made for has been collected (so in essence it’s not an expense on your income statement)
Db Allowance for doubtful accounts
Cr Expense from increasing the allowance for doubtful receivables

With the first entry you close the receivable balance as you would do on normal debt collection cases. The second entry is something more specific though. When you first recognize the write-down, it’s meant to show on your income statement that in fact your revenue is probably lower so hence you’ve recognized an allowance for the doubtful revenue (in essence you’ve decreased the revenue). However, when the balance is eventually received, it’s definite now that the revenue should have been recognized and with this your profit should also essentially be bigger, so what you do, you decrease the expense account. You recognize the “income” from the receivable on the same account you recognized the expense in the first place.