Prayer offered at home behind the imam is not valid.
It is not valid to pray with the imam who is in the mosque unless you are also inside the mosque, or you are outside the mosque but the rows are continual, such as when the mosque is full of worshippers and some of them pray outside, then their prayer is valid.
With regard to praying outside the mosque when there is room inside the mosque to pray, this prayer is not valid.
The Standing Committee was asked about a person who prays jamaa’ah in his house following what he can hear from the loudspeakers of the mosque, and there is no connection between the imaam and the person praying behind him, as happens in Makkah and Madeenah at the time of Hajj.
This prayer is not valid. This is the view of the Shaafa’is and was also the view of Imam Ahmad, unless the rows reach his house and he can follow the imam by seeing him and hearing his voice, in which case his prayer is valid, as is the prayer of the people in rows that reach his house. But unless this condition is met, his prayer is not valid, because what the Muslim is obliged to do is to offer the prayer in congregation in the houses of Allaah (the mosques) with his Muslim brothers. The Prophet (peace and blessings of Allaah be upon him) said: “Whoever can hear the call and does not come, there is no prayer for him, except for one who has an excuse.” Narrated by Ibn Maajah and al-Haakim; al-Haafiz said: its isnaad meets the conditions of Muslim. And the Prophet (peace and blessings of Allaah be upon him) said to the blind man who asked him about praying in his house, “Can you hear the call to prayer?” He said, “Yes.” He said, “Then answer it.” Narrated by Muslim in his Saheeh.
And Allaah is the Source of strength.
Fataawa al-Lajnah al-Daa’imah, 8/32.