Is the circulating story true regarding the Prophet, may God’s prayers and peace be upon him, imagining his mother after Abu Bakr Al-Siddiq, may God be pleased with him, was injured, and where was it mentioned?

This story has no basis and has not been mentioned by anyone who compiled works on the Prophet's biography. Scholars have stated that there was a companionship between Abu Bakr and the Prophet, peace and blessings be upon him, before the prophethood, and that when the Prophet, peace and blessings be upon him, offered him Islam, he did not hesitate. Ibn Hajar said in "Al-Isabah fi Tamyiz al-Sahabah": "He accompanied the Prophet, peace and blessings be upon him, before the prophethood, and was quick to believe in him."