The UN Report on Hariri vs The Guardian UK

     Page 10 of the report, which describes "the crime" in full, is as follows.

38. Shortly after the blast, the Director of Al-Jazeera TV in Beirut received a telephone call from a man who stated that the Nasra and Jihad Group in Greater Syria claimed responsibility for the assassination of Mr. Hariri. This message was broadcast shortly thereafter.

     That seems to be it.  This story in the Guardian, published very soon after the event, gives a lot more detail than the UN report.

Little more than half an hour after the explosion a man speaking in "poor Arabic, or just pretending to have poor Arabic" called the Beirut office of al-Jazeera television with a statement saying: "The Nasra & Jihad Group in Greater Syria claims responsibility for the execution of the agent Rafik Hariri, in the name of the oppressed, the Nasra and the Jihad."

A little later, Reuters news agency also received a call from a man described as "using a false Palestinian accent" and "shouting in an authoritative voice" who said: "Write down, write down and don't talk. We are the Nasra & Jihad group in greater Syria. On this day have given due punishment to the infidel Rafik Hariri, so that may be an example to others of his sort."

At 2.19pm a man speaking in "very good Arabic", phoned al-Jazeera and said a tape could be found in a tree near the UN building in Beirut. A member of al-Jazeera's staff went to look but failed to find it. A second staff member joined the search and the video was eventually retrieved.

The tape showed a bearded young man claiming responsibility for the assassination on behalf of the "Nasra and Jihad Group of Greater Syria".

...

In their first floor flat in the Arab University district of Beirut, Taysir Abu Adas and his family were also watching the television and they recognised the bearded young man as their missing son, Ahmad. Ahmad, of Palestinian origin, was 22 and unemployed. Three years earlier he had become deeply interested in religion and sometimes led prayers at the al-Huri mosque. About a month before Hariri's assassination he told his family he had met a "new friend" at the mosque.

Early on January 16, someone blew a car horn outside the family's flat and Ahmad went out, apparently to meet his "new friend". As he left, he borrowed LE2,000 (about 80p) from his mother and said he would be back in a few hours.

He never returned and was officially reported missing on January 19.