Frank ---
I could find no woman who was a fiancee of a Mr. Graves. But here are the names of unmarried women who died on the Titanic, and who embarked from Southampton, and who are not known to have been engaged to someone else. If anything, it is a start.
From Second Class:
Annie Funk, 38.
Marta Hiltunen, 18.
Henriette Yrois, 24. (She may or may not have been William Harbeck's mistress).
From Third Class:
Ida Andersson, 38.
Elin Braf, 20.
Marija Cacic, 30.
Manda Cacic, 21.
Gerda Dahlberg, 22.
Doolina Ford, 21.
Lillian Goodwin, 16.
Aloisia Haas, 24.
Alice Harknett, 21.
Wendla Heininen, 23.
Jenny Henriksson, 28.
Ida Ilmakangas, 27.
Pieta Ilmakangas, 25.
Katriina Jussila, 20.
Mari Jussila, 21.
Maria Kink, 22.
Kristina Laitinen, 37.
Agda Lindahl, 25.
Manta Nieminen, 29.
Marija Oreskovic, 20.
Jelka Oreskovic, 23.
Matilda Petranec, 28.
Ellen Petterson, 18.
Susanna Riihivuori, 22.
Stella Sage, 20.
Ida Strandberg, 22.
Augusta Vanderplancke, 18.
From the Crew:
Stewardess Katherine Walsh, 32.
I would recommend you check out the biographies for these women on this site. Often there are photographs included with the bio, and so you may be able to recognize or rule out some women. Also, many of these women I listed are immigrants from the Scandinavian and Eastern European countries heading to live in America permanently, and so are unlikely to have become engaged to an Englishman. I would also caution you that it is quite possible that the information inscribed on the painting is inaccurate.