what exactly happened to the broken tablets?

And it came to pass, as soon as he came nigh unto the camp, that he saw the calf, and the dancing: and Moses' anger waxed hot, and he cast the tables out of his hands, and brake them beneath the mount. (Exodus 32:19)

According to the "Torah" God inscribed the commandments with his finger Exodus 31:18. You’d expect Moses of his followers to pick up the broken pieces of the tablets and safeguard them since God himself wrote it, yet there is no information about the first set of the broken tablets.  What’s more interesting about the tablets is, the second rewritten tablets does not match with the first broken set which  causes Another issue with Ten Commandments monuments is that they contain the text of the Decalogue as found in Exodus 20, although it also appears in the Hebrew Bible in Deuteronomy 5. The two versions are different. For example, Exodus states:

Remember the sabbath day and keep it holy. Six days you shall labor and do all your work, but the seventh day is a sabbath of the LORD your God: you shall not do any work—you, your son or daughter, your male or female slave, or your cattle, or the stranger who is within your settlements. For in six days the LORD made heaven and earth and sea, and all that is in them, and He rested on the seventh day; therefore the LORD blessed the sabbath day and hallowed it.

while Deuteronomy reads:

Observe the sabbath day and keep it holy, as the LORD your God has commanded you. Six days you shall labor and do all your work, but the seventh day is a sabbath of the LORD your God; you shall not do any work—you, your son or your daughter, your male or female slave, your ox or your ass, or any of your cattle, or the stranger in your settlements, so that your male and female slave may rest as you do. Remember that you were a slave in the land of Egypt and the LORD your God freed you from there with a mighty hand and an outstretched arm; therefore the LORD your God has commanded you to observe the sabbath day.

If the hand written words of God can go missing, what about the “Torah” which was written by man?