Anas bin Malik narrated that:

A Jew came to the Prophet (ﷺ) of Allah and his Companions and said: “As-Samu Alaikum (Death be upon you).” So the people replied to him. The Prophet (ﷺ) of Allah said: “Do you know what this person said?” They said: “Allah and His Messenger know better – he said the Salam – O Allah’s Prophet.” He said: “No, rather he said like this and that. Bring him back for e=me.” So they brought him back and he said: “Did you say As-Samu Alaikum? He said: “Yes.” So with that Allah’s Prophet (ﷺ) said: “When one of the People of the Book gives you the Salam, then say: “Alaika Ma Qulta (Whatever you said to you too).” He said: ‘And when they come to you, they greet you with a greeting wherewith Allah greets you not.’

حَدَّثَنَا عَبْدُ بْنُ حُمَيْدٍ، حَدَّثَنَا يُونُسُ، عَنْ شَيْبَانَ، عَنْ قَتَادَةَ، حَدَّثَنَا أَنَسُ بْنُ مَالِكٍ، أَنَّ يَهُودِيًّا، أَتَى عَلَى النَّبِيِّ صلى الله عليه وسلم وَأَصْحَابِهِ فَقَالَ السَّامُ عَلَيْكُمْ فَرَدَّ عَلَيْهِ الْقَوْمُ فَقَالَ نَبِيُّ اللَّهِ صلى الله عليه وسلم ‏"‏ هَلْ تَدْرُونَ مَا قَالَ هَذَا ‏"‏ ‏.‏ قَالُوا اللَّهُ وَرَسُولُهُ أَعْلَمُ سَلَّمَ يَا نَبِيَّ اللَّهِ ‏.‏ قَالَ ‏"‏ لاَ وَلَكِنَّهُ قَالَ كَذَا وَكَذَا رُدُّوهُ عَلَىَّ ‏"‏ ‏.‏ فَرَدُّوهُ قَالَ ‏"‏ قُلْتَ السَّامُ عَلَيْكُمْ ‏"‏ ‏.‏ قَالَ نَعَمْ ‏.‏ قَالَ نَبِيُّ اللَّهِ صلى الله عليه وسلم عِنْدَ ذَلِكَ ‏"‏ إِذَا سَلَّمَ عَلَيْكُمْ أَحَدٌ مِنْ أَهْلِ الْكِتَابِ فَقُولُوا عَلَيْكَ ‏"‏ ‏.‏ قَالَ ‏"‏ عَلَيْكَ مَا قُلْتَ ‏"‏ ‏.‏ قَالَ ‏:‏ ‏(‏وإِذَا جَاءُوكَ حَيَّوْكَ بِمَا لَمْ يُحَيِّكَ بِهِ اللَّهُ ‏)‏ ‏.‏ قَالَ أَبُو عِيسَى هَذَا حَدِيثٌ حَسَنٌ صَحِيحٌ ‏.‏