All perfect praise be to Allah, The Lord of the Worlds. I testify that none is worthy of worship except Allah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and messenger.
The sum you paid as zakat-ul-Fitr on behalf of your friend, in response to her request, cannot be considered a charity on your own behalf. Moreover, it is invalid to consider a part of the money that you spent during Ramadan or any other time as zakat-ul-Fitr on her behalf. It is so because paying zakat requires having the intention to do. Since you have sent the sum, as she asked you to do, this is enough as intention and it is valid as zakat-ul-Fitr on her behalf. Thus, it is not valid to consider it charity on your behalf later on.
As for paying zakat-ul-Fitr after the expiry of its prescribed, fixed time, which is the time between Fajr and ‘Eed prayers, it is impermissible, whether one pays for himself or on behalf of others. It goes against the command of the Prophet, sallallaahu ‘alayhi wa sallam, who ordered zakat-ul-Fitr to be given before people go to the ‘Eed prayer. [Al-Bukhari and Muslim]
Whoever delays it after this time without a sharia-approved excuse has violated the order of the Prophet, sallallaahu ‘alayhi wa sallam. But if there is a sharia-approved excuse, such as a lack of zakat recipients, being doubtful about their status in terms of eligibility to receive Zakah, or finding no one to deliver it, then we hope that one is not blamed in this case.
Finally, it should be noted that zakat should not be given outside the country where the payer lives, unless there is a greater need or for a certain interest.
Allah Knows best.