Michaelis realised after rereading Anne's diary recently that there were no known pictures of Schiff, a museum spokeswoman said.
She said: "He read the diary in the 1950s and thought that Peter Schiff was very likely his friend.
"But it was only when reading it later that he saw there were no photos and so he contacted us."
Frank's Jewish family fled Nazi Germany in 1933 and settled in Amsterdam.
During the second world war the Nazis occupied the Netherlands and began deporting Jews to death camps in 1942, prompting the Frank family to go into hiding.
They lived in a secret annexe in a canal-side house for more than two years before their hiding place was betrayed and the family sent to concentration camps.
Anne recorded her years in the attic hideaway in her diaries.
A Dutch woman who helped the family found them in the annexe after Anne's arrest and gave them to her father Otto who survived the Holocaust.
They became famous around the world.
Frank said in her diary: "I forgot that I haven't yet told you the story of my one true love."
"Peter was the ideal boy: tall, slim and good-looking, with a serious, quiet and intelligent face," Anne wrote of the 13-year-old she had fallen for in 1940 when she was just 11.
The two youths would collect each other from school and walk hand in hand through their local neighbourhood.
Frank said: "He had dark hair, beautiful brown eyes, ruddy cheeks and a nicely pointed nose. I was crazy about his smile, which made him look so boyish and mischievous."
Peter later died in Auschwitz, while Anne died in Bergen Belsen concentration camp in 1945.
Anne last saw Peter a few days before she moved into the annexe, but wrote of him in her diary mamy months later after dreaming of him.
"I've never had such a clear mental image of him. I don't need a photograph, I can see him oh so well," she said.