Is this hadeeth saheeh (authentic)?
This hadeeth is not saheeh, and it is not proven from the Prophet (peace and blessings of Allah be upon him).
Al-Bayhaqi narrated in Shu’ab al-Eeman (3/1437) from ‘Abd-Allah ibn Abi Awfa (may Allah be pleased with him) that the Prophet (peace and blessings of Allah be upon him) said: “The sleep of the fasting person is worship, his silence is tasbeeh (glorification), his du’a (supplication) is answered and his good deeds will be multiplied.” Its isnad (chain of narration) was classed as weak by al-Bayhaqi who said: Ma’roof ibn Hassan (one of the men in the isnad) is da’eef (weak) and Sulayman ibn ‘Amr al-Nakha’i is weaker than him. Al-‘Iraqi said in Takhreej Ihya’ ‘Uloom al-Deen (1/310): Sulayman al-Nakha’i is one of the liars. It was classed as da’eef by al-Manawi in Fayd al-Qadeer (9293) and it was mentioned by al-Albani in Silsilat al-Ahadeeth al-Da’eefah (4696) who said: It is da’eef.
What the Muslims should do in general – and this applies even more so to khateebs and da’iyahs (callers to Islam) – is to verify reports before attributing a hadeeth to the Messenger of Allah (peace and blessings of Allah be upon him). It is not permissible to attribute to him anything that he did not say. He (peace and blessings of Allah be upon him) said: “Telling a lie about me is not like telling a lie about anyone else. Whoever tells a lie about me deliberately, let him take his place in Hell.” Narrated by al-Bukhari (1391) and by Muslim in the introduction to his Saheeh (4).
And Allah knows best.