"“Than whom,” said Dupin, amid a perfect whirlwind of smoke, “no more sagacious agent could, I suppose, be desired, or even imagined.”
..."See in text(The Purloined Letter)
In the context of Dupin’s previous encounters with Monsieur G— in Poe’s other Dupin stories, Dupin’s response to him here is humorous verbal irony, as Dupin always solves the cases that the Prefect can’t figure out.
"His lynx eye immediately perceives the paper, recognises the handwriting of the address, observes the confusion of the personage addressed, and fathoms her secret...."See in text(The Purloined Letter)
A lynx is a wild animal, a large solitary cat known for being a stealthy hunter with eyesight so strong that it can see the smallest of prey at 250 feet. Comparing Minister D—to a lynx indicates how he was able to read the address on the letter; also, it casts him as a stealthy predator, with the queen as his prey.
Choosing not to give this character a last name suggests that he is a real person whose identity is being protected, which adds more authenticity to the short story. In Paris, the Prefect of Police is the officer who oversees all police departments in the city.