Can you please tell me if we would use their or her as a possessive pronoun in this sentence?
Each of the girls in Mark's shop spent their money buying cakes.
Each of the girls in Mark's shop spent her money buying cakes.
'Their' would be more colloquial - except that a sentence beginning 'each of the girls' is never going to be colloquial; so use 'her'.
When one uses "each," one is intentionally singling out every individual member of the common group. To my mind, that fact screams for the use of singular pronouns.