In the opening scene of Jurassic World: Fallen Kingdom, a team inside a submersible collected a sample of the I-Rex's bone so that its DNA could be extracted. How did they know that the I-Rex was eaten by the Mosasaurus and its bones were at the bottom of the lagoon?
Owen or Claire were there when Mosauraus dragged Indominus into the lagoon. It's possible that they might have told someone what happened to I-Rex. Since it was a big tragedy and words travel fast, the authorities might know about it.
Now, all they have to do is to search that lagoon for indominous's remnants. If you notice, they were searching through lagoon before they reached its skeleton.
However, this is not shown how exactly Mosauraus ate I-rex, but by looking at the skeleton, he just ate it like a lion or a tiger do.