Is the Hadith: "Teach your children swimming, archery, and horsemanship" authentic or weak?

The author of Kanz al-Ummal mentioned a narration from Umar (may Allah be pleased with him) that he wrote to the people of Sham to teach their children swimming, archery, and horsemanship. No judgment was made on its authenticity or weakness. Two hadiths were narrated with the wording: "Teach your children swimming and archery" and "Teach your children swimming and shooting," both of which Al-Albani graded as weak. However, authentic hadiths have been reported regarding the virtue of archery, including: "Shoot, O sons of Ismail, for your father was a shooter" and "Indeed, strength is in shooting." Authentic hadiths have also been reported regarding the virtue of horses, including: "Goodness is tied to the forelocks of horses until the Day of Judgment." And an authentic hadith (definition) was reported concerning learning to swim, among them: "Everything that does not involve the remembrance of Allah is idleness and play, except for four... and a man teaching himself to swim."