Anas bin Malik narrated that:

A Jew came to the Prophet of Allah and his Companions and said: “As-Samu Alaikum (Death be upon you).” So the people replied to him. The Prophet 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 ﷺ وَأَصْحَابِهِ فَقَالَ السَّامُ عَلَيْكُمْ فَرَدَّ عَلَيْهِ الْقَوْمُ فَقَالَ نَبِيُّ اللَّهِ ﷺ " 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 ﷺ 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 .