Wa `alaykum as-SalamuwaRahmatullahiwaBarakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
There is no objection in the Shari`ah to pay double Zakat Al-Fitr at the place where you reside and at your home country.
Answering your question, Prof. Dr. Monzer Kahf, Professor of Islamic Finance and Economics at Qatar Faculty of Islamic Studies, states:
Yes, of course. It is allowed to pay more any amount. For instance, once the Prophet (peace and blessings be upon him) wanted to make Udhiyah (sheep sacrifice) at time of `Eid Al-Adha, he offered two big and good rams.
Also what you heard is inaccurate; it is better to pay it where you reside unless there is a good reason to send it to another place, your home land or any other country. Good reasons include people who are in more severe situations like refugees and displaced people or poor relatives, or people who suffer from calamities and the like.
Allah Almighty knows best.