My son has dual citizenship (US/Korean) and resides in Korea. We plan to visit US for a week in 2 weeks and found his US passport expires in March.
I understand that he will be allowed to enter US with his valid US passport, but am wondering whether he will be allowed to leave the country in Feb 10 with his US passport expiring in a month. The destination is South Korea where he resides, and has valid Korean passport.
Shall I apply for the expedited passport renewal service, or will it be OK to renew his passport after we return to Korea?

Korea->US Feb.3
US->Korea Feb.10
US passport expiration Mar. 10
Korean passport expiration 2020