Financial crime involving reporting a higher price than paid, receiving reimbursement, and pocketing the difference

However, the salesman inflates each expense by a small amount, 5-10%, and pockets the difference between the amount he is reimbursed and the amount he actually spent

This is meaningless.

Each expense would have to be accompanied by a real receipt.

Note that indeed the company ultimately needs that real paperwork to square their accounting and taxes.

Incredibly, the salesperson could be generating fake receipts (presumably using printers, etc).

That would be falsifying documentation.

As TTT explains, that is surely fraud.

If you want a more detailed investigation of the best legal terminology (in a given jurisdiction) ask on the excellent Law SE web site.

Again, what you ask is impossible - since expenses have to come with invoices.

To receive reimbursement, the salesman sends an invoice at the end of each month iterating each expense incurred during that month. However, the salesman inflates each expense by a small amount, 5-10%, and pockets the difference between the amount he is reimbursed and the amount he actually spent.

What you are describing is theft.

A company can require that 100% of expenses be documented, but in reality there are some expenses that won't have a receipt. Currently the IRS only requires expenses above $75 to be connected to a receipt or other proof. But a company can go beyond the IRS requirements, but if they meet the requirements the money isn't considered taxable income.

The issue for the company is not just the IRS requirement that the undocumented items should be considered as taxable income, there is also the issue of theft of company funds.

In places I have worked the list of allowable items that won't have a receipt is very small. Public transportation expenses is one item that can be reimbursed without a receipt, but then again the cost of each subway ride is only a couple of bucks.

One way to prevent some of the abuse is through the use of a company card, with the requirement that it be used exclusively for these expenses, and that all expenses be run through the card. That makes the real amount easier to get correct. There should still be a monthly requirement to connect every expense to a customer or potential customer.