"pro former" is a simple mistake. The correct expression is "pro forma."

Pro forma is latin and it means, at its simplest, "standard form."

The term is often used in a technically inaccurate way but which, through repetition, has become acceptable as a term of art.. This is in the sense "pro forma invoice."

A "term of art" is an expression that is in common use and widely understood even though it is not linguistically correct.

A pro forma invoice is not an invoice per se (more Latin! That one means "as such"). Actually, the document is used as a kind of "pre-invoice" which shows what the invoice will be when it's issued. This use has gained popularity since the introduction of tax systems under which a company is liable for, e.g. Value Added Tax when the invoice is issued. So the "pro forma invoice" is delivered and the formal invoice issued when payment is made. It can be viewed as a notice rather than an invoice.

The strict translation of "pro forma" is "for form." In this context the word "form" means style rather than a paper or computer form.