Sorry for my slow reply. (I am in the middle of business trip.)
I think the custom invoice and billing invoice has difference amount.
The import Tax that is calculated from custom invoice will be difference from import tax that calculated from billing invoice. This may cause problem if Auditor or custom officer found it.
That way I like to have only one invoice. I already explained to Pathom-san so he should consult with our accounting or related department then make decision with you.