Birth Certificate for parent

When I enquired with Lublin Archives about a birth certificate for my mother, I provided 2 different last names because I was not sure who the natural father was. The archives responded the a certificate could not be found under either last name. That suggests to me that the birth was not registered or the records may have been destroyed because of the war. My mother was born in 1942. I do have 4 scanned documents that I received from ITS that suggest her last name was Slyszko, since my grandmother was still married to her 1st husband at the time. My mother was, I assume, adopted, after my grandmother got an annulment of the 1st marriage and remarried 2 months after that. The replacement birth certificate (declaration made in Muensingen Germany) was issued with the 2nd husbands last name. What I would like to know, going by the 4 scanned documents with the other last name, how easy would it be to make and file a birth certificate for my mother? Who can I talk to in this regard and maybe help me to make an application to have her birth certificate registered. I know I am taking a chance assuming my grandmothers' 1st husband was the father, but I chance I need to take. Especially since I can't ask mother mother or grandmother since they are dead and I can't trust my aunts to tell me the truth since they lied and have been caught lying and their memories may not be accurate after all these years.