Bottom Line Up Front: I would probably modernize/anglicize the title as "Assistant Provost-Marshal" (of the Saxon Prince elector's Army)
finding it tough to succinctly explain how I arrived at that, so please bear with me...
Your sentence "lieutenant general in Saxon prince-elector's military police" gives the impression of an independent 'organization' within the army composed entirely of "police" and that this individual was a senior officer of the rank of Lieutenant-General in said organization.
A Provost was an individual appointment within a regiment with responsibility for overseeing discipline and punishment. They were assisted/understudied by a Provost-Lieutenant. The responsibilities of these positions are somewhat analogous to modern military police but their subordinates (the "provost guard") were typically not charged with any "police powers".
In addition to dealing with soldiers (and detainees/prisoners) the provost was also usually charged with overall responsibility for the train of "camp-followers" (women, children, merchants/sutlers, etc.) and it's discipline.
The General Staff of an army would include a General-Provost (best English term would probably be 'provost-marshal') who would perform the duties of the provost for the headquarters as well as being the staff officer responsible for all provost "matters". Now my inference (I haven't found any source that specifically mentions this position) is that the General-Provost would, similar to a regiment, have an assistant/understudy which should logically be called a GeneralProvostLieutenant.
Now as to the rank of Lieutenant-General... A lieutenant-general would be second only to "the" general (aka Captain-General) a higher rank than this individual likely held. The inclusion of General in the appointment title typically does not mean the individual was ranked as a General, but that they had the authority of a General (within their specific area of responsibility). From looking over some period Prussian pay lists it appears a General-Provost was roughly equivalent to a Colonel (Dem Obersten) so if I had to assign a modern English rank to Viet Criel I would go with Lieutenant-Colonel.
Hope that explains my initial answer without meandering too far afield and without being overly confusing.