The Hadith: 'Teach your sons swimming and archery...'

Q: Can you please clarify who said the following words, for some of our teachers say it is a Hadith, while others attributes them to one of the Sahabah (Companions of the Prophet): “Teach your sons swimming, archery and horsemanship.” I hope that you will send us the correct answer with citing its sound Sanad (chain of narrators), and may Allah reward you with good.

(Part No. 4; Page No. 437)  A: This Hadith is related by Al-Bayhaqy on the authority of Ibn ‘Umar (may Allah be pleased with them) from the Prophet (peace be upon him), with the following wording: “Teach your sons swimming and archery, and teach woman how to spin.” It is also related by Al-Daylamy in: "Musnad Al-Firdaws" on the authority of Jabir who narrated it from the Prophet (peace be upon him) with the following wording: “Teach your sons archery, for it is a means of defeating the enemy.” The Sanad includes ‘Abdullah ibn ‘Ubaydah who is stated by Al-Dhahaby in his book "Al-Du‘afa’ (Weak Narrators)" and he said: He is Da‘if (weak) narrator, but more than one scholar consider him to be Thiqah (trustworthy). The Sanad also includes Mundhir ibn Ziyad, concerning whom Al-Daraqutny said, “He is Matruk (a narrator whose Hadith transmission was discarded due to unreliability).” This Hadith is also reported by Ibn Mandah in: "Al-Ma‘rifah", Abu Musa in: "Al-Dhayl", and Al-Daylamy in: "Musnad Al-Firdaws" on the authority of Bakr ibn ‘Abdullah ibn Al-Rabi‘ Al-Ansary from the Prophet (peace be upon him), with the following wording: “Teach your sons swimming and archery! How excellent entertainment for woman in her house is the spin! And if your parents call you, answer to your mother (first).” The Sanad of this narration includes Sulaym ibn `Amr Al-Ansary concerning whom Al-Dhahaby said in: "Al-Mizan", "`Aly ibn ‘Ayyash reported a false narration from him" and he quoted this Hadith.However, learning archery is lawful as indicated by many Sahih Hadith (a Hadith that has been transmitted by people known for their uprightness and exactitude; free from eccentricity and blemish). It also falls under the general meaning of the Ayah saying (what means): And make ready against them all you can of power May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.