Buy the new ticket, it's already too late for the old one.
The above is intended only as general information, and does not constitute legal advice. You must speak with an attorney to discuss your individual case.
Mr. Berman is correct ... buy a new ticket that departs prior to June 5th.
You probably couldn't have extended the prior ticket anyway ... the best pricing is usually on tickets that have a 6 month maximum validity.
With that said you can call the airline ... sometimes they will give you a credit on the unused 1/2.
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.
I agree with prior responses. USCIS wants to see proof of your mother's intent to return home. Buy her a plane ticket for sometime prior to June 5th amd aemd them a copy of it.
The answers offered here are purely informational and do not create an attorney-client relationship. For more detailed information or to schedule a consultation please contact our office at (718) 924-2896.