It is pretty common to send an offer by the last minute

At one time, the deadline to make an offer for a listing was 5:00pm. I tried to send the offer by 4:45pm, the the fax machine of the listing agent had been busy, so I scanned the offer and sent by 4:55pm, and the email went through by 4:58pm or so (cannot remember all the details).

But, by the same time, some agents make false claims of multiple offers.
In this past October, our offer for a half million dollar house was accepted. We were sitting on the table to initial several pages to ratify it.

Then the listing agent called and told me she got another offer which was five thousand dollars higher than ours.

I adviced my clients not to add any money and prepare to give it up.

A few minutes later, the listing agent called again and told me that the seller still wanted to work with us. So I sent the fax in and ratified it.

I really doubt that offer existed.

For the false offer, it is hard to prove as the listing agent is not supposed to release information of the other offers.

If you can prove it, you can either complain to the board or sue him/her in the court. Though s/he would not lose his/her license immediately, but will get a big dent.