Accidently processed a payment under wrong customer, is there a way to move that payment into a different invoice where it belongs or do I have to void the payment

You can unlink the processed payment then recreate it again to apply them to the correct invoices, Service59.

In QBO, if the payment was applied to the incorrect invoice, we can delete the payment transaction for the invoice to be tagged as Open. Then, create a receive payment entry again and link it to the right invoice. Let me guide you how:
 

1. In your QBO account, go to the Sales menu and select the All Sales section.
2. Find the payment transaction and click Edit to open it.
3. You'll be routed in the Received Payment page.
4. Then, click on the More at the bottom and choose Delete.
5. You'll be prompted with Are you sure you want to delete this? Click Delete Transaction.

Once done, you can now create a payment and apply it to the correct one. Feel free to check out this article for additional guidance: Record invoice payments in QuickBooks Online.

You may also utilize this link for another way of correcting payments: Fix a payment applied to the wrong invoice in QuickBooks Online.

Moreover, I've added these references to help you track your overall sales transactions and review your account:
 

• Run a report in QuickBooks Online
• Reconcile an account in QuickBooks Online
   

Lean on us for any additional assistance when managing customer payments in your account. Our team is always around to ensure you succeed. Stay safe!