Praise be to Allah.
There is nothing wrong with that. There is nothing wrong with slaughtering the ‘aqeeqah on their behalf, even if they have passed the age of four years, although it would have been better to hasten to do it. But if it has been delayed, then there is nothing wrong with doing this; he may slaughter it whenever he can afford to do that.
With regard to where the ‘aqeeqah is slaughtered, there is no specific place for that; rather it is permissible to slaughter it in the city where they were born, or elsewhere, because it is an act of worship for which no place is specified.
With regard to eating the meat, the ‘aqeeqah comes under the same ruling as the udhiyah (sacrifice); it is mustahabb for the one who offers it to eat from it himself, to give some in charity, and to give some as gifts to his neighbours and friends.
End quote from Majmoo‘ Fataawa ash-Shaykh Saalih al-Fawzaan (2/572)
And Allah knows best.