Let $Q$ be a compact Riemannian manifold. Then $\Lambda Q\rightarrow Q,$ $\gamma\mapsto \gamma(0)$ can be shown to be a locally trivial fiber bundle of Hilbert manifolds. Here, $\Lambda Q$ denotes the space of maps $S^1\rightarrow Q$ of Sobolev class $W^{1,2}.$

Question: Who proved it first? Is there an appropriate reference?

I once read it attributed to Klingenberg, but didn't find the proof (nor the statement) in the corresponding reference. I only know a proof due to Abbondandolo/Schwarz, but they claim no originality when asked.