The "Belle Greene" in question may be Isabel Colton Greene of Nashua, NH
who is documented in the online Union Catalog of Letters as corresponding
with Clemens.  The letters database is online at:

http://www.marktwainproject.org

This "Belle Greene" is Isabel Colton Greene (b. 1842 - d. 1926) who was a
writer. Clemens owned at least one of her novels _A New England
Conscience_.  Her spouse was Martin Van Buren Greene of NH.  There is a
photo and biographical profile online of her in google books in _A Woman of
the Century_ by Frances Elizabeth Willard, p. 337.

Barb