Is prayer accepted in the mosque, and must it be repeated after speaking with one's mother during Friday prayer?

Acceptance of prayer is known by Allah Almighty alone, and the correct question is about its validity. Your prayer is valid and sufficient, and you are not required to repeat it. However, you missed the reward of Jumu'ah because of talking during the Khutbah (definition) (sermon). It has been narrated that the Prophet, peace and blessings be upon him, affirmed Ubayy ibn Ka'b when he said to Ibn Mas'ud: "You have nothing from your Jumu'ah except what you babbled," and this means missing the reward of listening, not the invalidation of the prayer.