Rav Noach Isaac Oelbaum takes this idea a step further:
The pasuk says of the Arbeh, וינח, they rested, which the Ba’al HaTurim connects to the pasuk, וינח ביום השביעי – “And He rested on the seventh day”, indicating that the Arbeh rested on Shabbos.
Moshe witnessed the work that the Jews were subjected to in Mitzrayim. He saw their pain firsthand. “It happened in those days that Moshe grew up and went out to his brethren and observed their burdens” (2:11). He recognized that the labour was harsh and backbreaking. The Medrash (Shemos Rabbah 1:28) tells us that he went to Pharaoh to plead on behalf of the Jewish people. He argued that if the slaves had to work so intensely daily, then they would not be able to continue to work. They would collapse from fatigue and perhaps die of exhaustion. If Pharaoh wanted to maintain an active workforce, he would be wise to grant them a day off, a day of rest, once a week.
Pharaoh acquiesced, seeing the wisdom in Moshe’s words. Desiring to keep the slaves healthy and capable of work, he asked Moshe what day he thought the workers should have off. Moshe suggested that Shabbos be designated as the weekly day of rest, the day on which the slaves could rejuvenate themselves somewhat for the week ahead.
On Shabbos morning, In Shacharis, we recite, ישמח משה במתנת חלקו, Moshe rejoiced in the gift of his portion: in Shabbos. Why would Moshe rejoice specifically in the gift of Shabbos? Because he had already been mechadeish Shabbos as a day of free work before Hashem had ever given the mitzvah of Shabbos to the Bnei Yisroel.
Resting on Shabbos in Mitzrayim was the invention of Moshe Rabbeinu; it was his idea. When he then had his second chiddush and conceived the Makkah of Arbeh, both of these chiddushim were combined; thus, the Arbeh rested on Shabbos.
(Adapted from a much lengthier idea R’ Doniel Gladstein brings in his sefer, “The Light and the Splendor”, on Tu B’Shvat)
