וַיִּכְתֹּ֥ב מֹשֶׁ֛ה אֶת־הַשִּׁירָ֥ה הַזֹּ֖את בַּיּ֣וֹם הַה֑וּא וַֽיְלַמְּדָ֖הּ אֶת־בְּנֵ֥י יִשְׂרָאֵֽל׃
So Moses wrote this song the same day, and taught it the children of Israel.
Targum Jonathan on Deuteronomy
And Mosheh wrote this hymn, and taught the children of Israel.