Family #33 in the 1767 Grimm census.
Family #112 in the 1775 Grimm census.
According to the 1767 Grimm Census, Friedrich and his wife Maria Elisabeth came from Holstein, an area in what was then part of Denmark. This suggests that he may have been one of the German immigrants who first went to Denmark, and then later immigrated to Russia. A search of Danish records shows several Marquardts, but none named Friedrich. 
His wife Maria Elisabeth was first married to Jakob Hessenbeie. The two had a child, also named Jakob Hessenbeie, who was born about 1760. Her first husband's death is implied but not confirmed by specific language in the 1767 census. Typically a record for a widow or a child would have language that included the word "orphan" or it would designate his mother as the "widow of the [deceased's name]". There is also the possibility that the child was the son of a previous wife of Friedrich Marquardt, a woman who had been previously married to Jakob Hessenbeie before she married Friedrich Marquardt. This is a more complex theory, and many things have to have happened for it to be true. Sometimes, the right solution is the simplest solution.
There is no Hessenbeie surname in the Kulberg Reports, so it seems most likely that Jakob Hessenbeie the elder passed away in Germany, prior to his wife and son immigrating to Russia, probably under the surname Marquardt.
It should be noted that there is also no Friedrich Marquardt in the Kulberg Reports. Either he traveled under a different name, or he was left off the immigration lists for one reason or another.
1767 Grimm Census 
Also living with Friedrich and his wife was his step-son, Jakob Hessenbeie, who was born about 1760, probably in Germany.
1775 Grimm Census 
He does not appear in the 1798 census. He and his wife very well may have moved to a different colony. He also may have passed away. Had he survived, he would have been 63 years old.
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