The simple answer is no. The patients should consider herself immunized. Studies show that getting a delayed second dose doesn't necessarily increase antibody response, and there's some concern that it might actually have a negative effect on the immunity. If you've already had the regular seasonal dose, wait until next year for another dose.
Image of the H1N1 Influenza Virus, CDC.
From CDC's Immunize.org website:
Sometimes patients age 65 years and older who have received the standard-dose influenza vaccine hear about the high-dose product (Fluzone High-Dose, sanofi) and want to receive that, too. Is this okay to administer?
No. ACIP does not recommend that anyone receive more than one dose of influenza vaccine in a season except for certain children age 6 months through 8 years for whom two doses are recommended.
Would giving an older patient 2 doses of standard-dose influenza vaccine be the same as administering the high-dose product?
No, and this is not recommended.
New High-Dose Flu Shot for Older Americans: Answers to Flu Season Questions - AARP http://buff.ly/1ttjluQ
Ask the Experts about Influenza Vaccines - CDC experts answer Q&As; http://buff.ly/1ttjn6e
Fluzone High-Dose Seasonal Influenza Vaccine | Seasonal Influenza (Flu) | CDC http://buff.ly/1ttjnTu