My initial fax was on 1/8. Never received a response.
Emailed on 1/16. My partner was matched to 1P (from DL PM) on the same day. Hint: use email [email protected] for UA status matches and attach a PDF of all documentation.
The response below was received on 1/16:

Thank you for your e-mail.

Congratulations! You have been awarded Premier Executive status in the Mileage Plus program! This will make your travel with us comfortable, simple and more rewarding than ever.

Your status will be effective for 90 days. To keep the status through February 2009, just earn 15,000 base flight miles or 18 base flight segments on United, Ted or United Express within 90 days of being granted Premier Executive status. Once you meet that threshold, a Premier Executive kit will be generated and mailed. Until you have a card, be sure to add your Mileage Plus number to your reservation in order to fully benefit from your elite status.

To maintain the status throughout all of 2009, you must earn 50,000 Elite Qualifying Miles (EQM) or 60 Elite Qualifying Segments (EQS) between January 1, 2008 and December 31, 2008. EQM and EQS are earned on United, United Express, Ted and the Star Alliance members. For a current list of Star Alliance member airlines, please visit www.united.com/staralliance or www.staralliance.com.

For details about the Mileage Plus elite program, visit www.united.com/elite. I hope you will travel with us often and experience the exceptional service and style reserved for our elite members around the world.

Thank you for choosing United, and enjoy your Premier Executive membership.

He shouldn't have a problem with the requirement, thanks to our upcoming SFO-AKL trip.