Yes, the employer can file for him while he is still in the US. Yes, he can file for an extension but is unlikely to receive one.
The answer provided is general in nature and should not be construed as legal advice as not all facts are know by the attorney, nor does the answering of this question create an attorney client relationship.
Although they can file in April, he can't get an H-1B before October 1, 2014 ... far longer than his B-1 is currently valid ... and, it will be unwise to try to extend the B-1.
He should enjoy his vacation and go home to get the H-1B ... returning in October.
PROFESSOR OF IMMIGRATION LAW for over 10 years -- This blog posting is offered for informational purposes only. It does not constitute an attorney-client relationship. Also, keep in mind that this is an INTERNET BLOG. You should not rely on anything you read here to make decisions which impact on your life. Meet with an attorney, via Skype, or in person, to obtain competent personal and professional guidance.