Lee McCarthy, 31, told the High Court in Glasgow that he sent the message to Angela Sharkey on the social network to “try and get closure for her”.
He sent the message four months after a fire at her home which killed her husband Thomas Snr, 55, and their two children, Thomas Jnr, 21, and eight-year-old Bridget.
Mrs Sharkey, 48, was the only survivor.
The witness sent the message on the same day he made a police statement, one of many in the months after the fatal fire.
Cross-examining Mr McCarthy, who was in the witness box for a fourth day, Donald Findlay QC asked him if his statement helped bring Mrs Sharkey closure.
Mr McCarthy replied: “No.”
Scott Snowden, 37, and Robert Jennings, 50, deny murdering three members of the Sharkey family by pouring petrol or something similar through their letterbox and setting fire to it.
The two children died in the blaze at their home in Helensburgh, Argyll, in the early hours of Sunday July 24 2011. Their father died of his injuries in hospital six days later.
Between them Snowden and Jennings face 22 charges, all of which they deny.
Both men have lodged special defences of incrimination and alibi. Snowden claims he was in Mexico when the fire was allegedly started, while Jennings claims he was at home in Helensburgh.