I agree 100% with you, TNB. She was approved to take this time off to go to the funeral, right? So the stuff that needs doing should be able to wait or be reassigned to someone else. Is there someone else who has the authority to sign? Like her boss or another supervisor, etc? I don't know the situation on your work, so forgive me if she's the top of the food chain.
Does this invoice require a wet signature or could she sign it and fax/e-mail the signed invoice back to you? I have students nationwide that I need paperwork from regularly. If I need a wet signature, I'll overnight it out to them to sign and enclose a pre-paid overnight envelope so they can mail it back to me quickly without having to come up with the money on their own.
If we can make do without a wet signature, then I usually scan it and send it in an e-mail. Then they can print it out, sign it, and either scan it and e-mail it back to me, fax it, or take a picture with their phone and e-mail the picture to me.
ETA: I realized my post looks contradictory. I don't think this needs to be taken care of while she's off. BUT if it absolutely positively cannot wait and they make you contact her to get it signed, then that's what my different method's were detailing.