Ibn Hibban with two chains narrates that the messenger said: "Every important matter that does not begin with in the Name of Allah, the most Gracious the most Merciful is not complete.
Abu Dawud, Ibn Majah and Ibn Hibban from Kurrah ibn Abdurrahman from Zuhri from Abu Salamah from Abu Huraira from the prophet that he said: " Every important matter that does not begin with praise be to Allah or with thanking Allah is incomplete.
Ahmad narrated: " Every important matter that does not begin with mentioning the name of Allah, is considered incomplete".
Darakutni from Abu Huraira that: " Every important matter that does not begin with the name of Allah is incomplete".
Ibn Hajar in "Fathul-Bari" and Sujuti in "Ed-Darul-Manthur" narrated: " Every important matter that does not begin with the name of Allah is considered deprived".
The hadeeth referred to in the question is the hadeeth of Abu Hurayrah (may Allah be pleased with him) who said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “Every important word or matter that does not being with remembrance of Allah is maimed.”
And the hadeeth with narrated in other, similar versions.
It was narrated by Imam Ahmad in al-Musnad (14/329) [Mu’sasat al-Risaalah edn.] and by many other authors of Sunans and Musnads.
There are two things wrong with it:
The weakness of Qurrah ibn ‘Abd al-Rahmaan. Ahmad ibn Hanbal said: He is munkar al-hadeeth jiddan (i.e., a very weak narrator). Yahya ibn Ma‘een said: [He is] da‘eef al-hadeeth. Abu Zar‘ah said: The hadeeths that he narrates are munkar.
See: Tahdheeb al-Tahdheeb, 8/373
Some of the scholars think it more likely that the correct view concerning it is that in the report from al-Zuhri it is mursal, and mursal is one of the categories of da‘eef (weak) hadeeths.
It was narrated by al-Nasaa’i in ‘Aml al-Yawm wa’l-Layla (495, 497) from al-Zuhri. He said: The Messenger of Allah (blessings and peace of Allah be upon him) said:… and he narrated it.
Al-Daaraqutni (may Allah have mercy on him) said:
The correct view is that saheeh reports from al-Zuhri are mursal. End quote.
It was also classed as da‘eef by al-Zayla‘i in Takhreej al-Kashshaaf, 1/24 and by Shaykh al-Albaani in Irwa’ al-Ghaleel (1/29-32). And it was classed as da‘eef by the commentators on the Mu’sasat al-Risaalah edition [of Musnad Ahmad].
The hadeeth was classed as hasan or saheeh by a number of scholars. It was classed as hasan by al-Nawawi and Ibn Hajar, and it was classed as saheeh by Ibn Daqeeq al-‘Eid and Ibn Mulqin.
Shaykh Ibn Baaz (may Allah have mercy on him) was asked about it and said:
This hadeeth was narrated via two or more isnaads by Ibn Hibbaan and others. Some scholars classed it as da‘eef, but it is more likely to be hasan because of corroborating evidence (hasan li ghayrihi). End quote.
Majmoo‘ Fataawa Ibn Baaz (25/135)
The meaning of the hadeeth is acceptable and applicable. Allah opens His Book with the Basmalah, and Sulaymaan (peace be upon him) opened his letter to the Queen of Sheba (Saba’) with the Basmalah. Allah says (interpretation of the meaning): “Verily, it is from Sulaymaan (Solomon), and verily, it (reads): In the Name of Allaah, the Most Gracious, the Most Merciful” [al-Naml 27:30]. The Prophet (blessings and peace of Allah be upon him) opened his letter to Heraclius with the Basmalah, and he used to start his khutbahs with praise and glorification of Allah.
Most of the fuqaha’ are of the view that it is prescribed and mustahabb to say the Basmalah when starting important things.
It says in al-Mawsoo‘ah al-Fiqhiyyah (8/92):
Most of the fuqaha’ are agreed that saying the name of Allah is prescribed for all things of importance, both acts of worship and other things. End quote.
And Allah knows best.