The phrase "corresponding *" is correct and can be used in written English.
It is typically used to refer back to a previous noun or idea that is related or similar to the current one. Example: "John received an invitation to the conference, and he responded with his corresponding attendance form." Here, "corresponding" is used to show that the attendance form is related to the invitation that John received.
Exact(60)
We were corresponding before that.
He stroked the corresponding limb.
We began corresponding, sending pictures.
Look at his corresponding album.
So is the corresponding behaviour.
"The corresponding real cuts directly reduce GDP.
Each response has a corresponding emoji.
The corresponding phases for building a voice?
Each bottle bears its corresponding pie recipe.
There are no corresponding rights for citizens.
The corresponding number in 1997 was 228.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com