Definition of "addresser"
A person who addresses someone (directs spoken or written communication toward someone).
Quotations
All adults had to be addressed as Mister, Missus, Miss, Auntie, Cousin, Unk, Uncle, Buhbah, Sister, Brother and a thousand other appellations indicating familial relationship and the lowliness of the addressor.
1969, Maya Angelou, chapter 5, in I Know Why the Caged Bird Sings, New York: Bantam, published 1971, page 22
A person who addresses (applies an address to an object to be delivered to a particular location).
Quotations
[…] if they had not been lifted in the air by the enormous accident of a man of genius, the Dickenses, I fancy, would have appeared in poorer and poorer places, as inventory clerks, as caretakers, as addressers of envelopes, until they melted into the masses of the poor.
1906, G. K. Chesterton, chapter 2, in Charles Dickens: A Critical Study, New York: Dodd Mead & Co., page 25