How do I record invoices in my accounts (and VAT) that I've raised invoices for but not raised via quickbooks?

I've got the steps on how you can add the past transactions, marissa-leadersm.

Let me guide you with these steps:

If you received the payment the same day you send out the transaction, you can create a Sales receipt. 

1. From the + New button, select Sales receipt.
2. Select a Customer.
3. Filter the date to when the transaction happened.
4. Enter the PRODUCT/SERVICE, QTY, RATE, AMOUNT, and VAT.
5. Click either Save and new or Save and close.

If you received the payment at a later time, an invoice would be best to this. Here's how:

1. Select Invoice from the + New button.
2. Select a Customer.
3. Modify the Invoice date to when you send out the item.
4. Select the PRODUCT/SERVICE, QTY, RATE, AMOUNT, and VAT.
5. Click Save and new or Save and close.

I've also added this article on how to record their payment: Record invoice payments in QuickBooks Online.

That should do it. Let me know if ever you need extra help in recording customer payments. I've got your back!