Sir
We agree that "must" has many different uses, don't we?
Therefore,
As for reporting "must" with the meaning of obligation
1- to keep it unchanged if the obligation is still in practice
2- if the obligation has changed with the course of time, then it should be changed into " had to"
that's according to what has been tackled in"
Focus English Grammar
As for most book , they side with the ultimate change
That's God knows best
Regards