I guess your cousin does not have a certified copy from the birth register (see my post on this board regarding birth entries). This will not only tell the name of her mother and her address in 1955, but most probably also her date and place of birth. She must prove her descendancy and identity in that letter to the Standesamt of her birth town.
So first apply for a certified copy from the birth register.
Once it provides her mother's date and place of birth she should ask for that birth record also. this will hopefully tell when she got married and if she passed away that date and place.
I did this kind of research for US adoptees a few times last year and can certainly help her, but the municipalities charge for their services and I do not have much time presently.
Gaby