The phrase "corresponding with the" is grammatically correct and can be used in written English.
It is often used to show a connection or similarity between two things. Example: "The data in this graph corresponds with the information in the table."
I'd been corresponding with the band a little on Facebook, trying to get a read on their politics.
And so, corresponding with the end of any reported sightings of my father, we began to fear the worst.
Problems were at their worst in the south, south-west and Appalachia, corresponding with the poorest states in the union.
Recently, he began corresponding with the daughter of Lily Boeykens, the country's most prominent feminist, who asked for euthanasia because she showed preliminary signs of Alzheimer's.
The "unsettling" dark tale sees the main character, Zoe, corresponding with the prisoner in order to get her own dark secret and guilt off her chest.
"I have a feeling that there's probably a fairly large number of memorabilia corresponding with the big companies, like Pets.com, so there'll be a plentiful supply.
They maybe had a radical formal language, corresponding with the architecture, but then the architecture changed and the language ceased to be radical.
In early 2004, private investigators began corresponding with the stalker, sending spoofed e-mail back to him in the voice of a MicroPatent lawyer.
They're currently corresponding with the BBFC over how many times they can use the c-word in The World's End without forfeiting a 15 certificate.
So in February 2003, Mr. Cohodes started corresponding with the S.E.C. about NovaStar.
The historical religions fall into three great divisions, corresponding with the stages of the dialectical progression.
