I am looking for name of a movie about two historical researchers who find a love letter from a famous dead poet. Action goes back and forth from modern times to times of the poet as the plot unfolds

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Movie I believe is set in England and famous dead person could be a writer rather than a poet, perhaps in the late 19th Century

do the characters in modern day write back and forth with poet from past through letter in desk?

No. that’s a different movie. In this one they retrace the physcial movements that the writer made with his (presumed) lover and as they’re showing you those modern stpes they “flash back” to the actual movements of the historic people and what “really” happended