Both Uses of

correspond
in
And Then There Were None

…. and his correspondent signed herself with a flourish his ever Constance Culmington.
p. 2.8 *

correspondent = someone who communicates in writing

It corresponded only too well with the deep wound in the back of Rogers' head…
p. 185.3 *

corresponded = fit together

Definitions:

(1) (correspond as in: corresponding time period)
connect or fit together by being equivalent, proportionate, or matched

(Two things are equivalent if they have the same or very similar value, purpose, or result.)
(2) (correspond as in: corresponding by email)
communicate -- typically by writing letters or email

A corresponding secretary is an officer of an organization who is responsible for managing the organization's correspondence and keeping a record of it.
(3) (correspondence as in: a correspondence course)
done from afar

For example, a corresponding member or a correspondence course.

This sense of corresponding arose because people who lived in distant cities and could not be present for meetings, could communicate by sending written communications.
(4) (correspondent as in: foreign correspondent of the paper)
a reporter or other representative -- typically from a foreign country or with a particular expertise