How to book an invoice without a customer's Tax ID?

Alright, let's look at a hypothetical scenario: say I've got some clients visiting from Germany, we're sitting in a coffee shop, and the bill comes out to $167. Now, I didn't specifically ask for a formal business receipt—meaning my company's Tax ID isn't listed on the slip. Is there any way for me to get reimbursed by the company, and subsequently have that expense recorded and recognized in the books?

Here's a second situation: this isn't even about client entertainment. My mouse dies, so I head downtown and pick up a new one for $33. I just take a standard consumer receipt—again, no corporate Tax ID on there. Is it actually possible for the company to reimburse me for that, process the receipt, and book it as a legitimate business expense?

Obviously, in both of these cases, I can't claim any sales tax credit since the Tax ID is missing.

Generally speaking, you shouldn't. It isn't just about sales tax; it's also about which expenses the IRS actually recognizes versus what they don't, and how that mess impacts your bottom line and your corporate income tax.