Should he offer ‘aqeeqah for a baby who died immediately after birth?

Praise be to Allah.

It is prescribed to offer ‘aqeeqah for her, because of the general meaning of the evidence concerning that, which includes the following: 

1 – It was narrated from Salmaan ibn ‘Aamir (may Allaah be pleased with him) that the Prophet (peace and blessings of Allaah be upon him) said: “Every child should have his ‘aqeeqah, so shed blood for him and wipe the dirt away from him.” Narrated by al-Tirmidhi, 1515; al-Nasaa’i, 4214; classed as saheeh by Shaykh al-Albaani (may Allaah have mercy on him) in al-Irwa’, 4/396. 

2 – It was narrated that Samurah ibn Jundub (may Allaah be pleased with him) said: The Messenger of Allaah (peace and blessings of Allaah be upon him) said: “Every child is in pledge for his ‘aqeeqah, so slaughter (the sheep) for him on the seventh day, and give him his name, and shave his head.” Narrated by al-Tirmidhi, 1522; al-Nasaa’i, 4220; Abu Dawood, 2838. classed as saheeh by al-Albaani (may Allaah have mercy on him) in al-Irwa’, 4/375. 

If it is not appropriate to invite people to gather for the ‘aqeeqah meal because the infant has died, then you can give some in charity, eat some and give some as gifts.