If you don't need to print the invoice with the correct information (under the correct customer), and only transfer that balance, that is easier (/M credit and /M invoice, using a suspense GL account).  I would not do this if you are invoicing products (especially lot / serial items) which may need to be later traced back to the correct customer.

You don't need to create an SO for re-invoicing, and you'd really only want to do that if SO history means something to you (or if there is something left on back order).

The most complete fix is to credit the "bad" invoice fully, then re-create the invoice correctly.  For item costs related to FIFO / LIFO valuation , the costing amounts (CM vs IN) may be off by a bit, but there is no control over that.

If you don't need to print the invoice with the correct information (under the correct customer), and only transfer that balance, that is easier (/M credit and /M invoice, using a suspense GL account).  I would not do this if you are invoicing products (especially lot / serial items) which may need to be later traced back to the correct customer.

You don't need to create an SO for re-invoicing, and you'd really only want to do that if SO history means something to you (or if there is something left on back order).

The most complete fix is to credit the "bad" invoice fully, then re-create the invoice correctly.  For item costs related to FIFO / LIFO valuation , the costing amounts (CM vs IN) may be off by a bit, but there is no control over that.