All that can presently (December 2022) be gleaned about
Effie Brooklin from sheet music covers and by Internet searching is that she was presumably an American actress/singer who has been featured on 4 works published between 1901 and 1904.
Her portrait on the left is taken from
Many an Honest Heart May Beat Beneath a Ragged Coat (1901) music by
Arthur Trevelyan, words by Hawley Franck and published by
New York Journal, New York, USA. There, her surname is given as Brooklyn.
Surfers are welcome to contribute any further information about this performer.