I think you can book for others, not a problem
I'm not sure on FHR though, as there's benefits involved and they may want to see the actual AMEX Card
Even more, you can ask that person to sign the PTS form and write you down as 3rd party authorizer to book on their behalf
My bro authorized me and I booked hotel for myself using his $200 credit no problem
AMEX just wanted to see the form signed, his CC scanned front & back, called me to book over the phone
Loving mistake fares - Wideroe $250 to Italy, Delta $500 to ICN, Aeroplan 50K J to IST.
Loving AMEX welcome bonuses - 2000 Air Miles, 20K SPG points