According to the shrine, the blade is Kamakura period, the Koshirae is Nanboku-chō period, and that the koshirae was likely made specifically for the donation. I presume it was donated at that time, but there is no mention of how/when it was donated. Stylistically it is not a Momoyama period Tachi Koshirae in my opinion, there are many extant examples that can be drawn from for comparison. There is another example donated to the same shrine (image below), that is quite similar stylistically, that was said to have been donated Ashikaga Yoshimitsu in the same period. It is not a smoking gun, but I think worthy of discussion.