If the imam says one taslim, is it permissible for the one who is praying behind him to say two?

The imam should not limit it to only one taslim at the end of the prayer, because the second taslim is prescribed and doing it is preferable. In fact Imam Ahmad and some of the Maalikis are of the view that it is obligatory, and that the prayer is not valid without it. However the majority of scholars are of the view that the second taslim is Sunnah and mustahabb (encouraged). 

According to the view of the majority, limiting it to one taslim does not render the prayer invalid. 

If the imam says one taslim, there is nothing wrong with the one who is praying behind him saying the second taslim, because doing that is more complete and is more on the safe side, and it avoids an area in which there is a scholarly difference of opinion. 

The well-known view of the madhhab of Imam Maalik is that the one who is praying behind the imam should say two taslims, as will be explained below. 

An-Nawawi (may Allah have mercy on him) said in al-Majmoo‘ (3/462): The correct view according to our madhhab is that what is preferred is to say two taslims. This is the view of the majority of scholars among the Sahaabah and Taabi‘een, and those who came after them. This was narrated by at-Tirmidhi, al-Qaadi Abu’t-Tayyib and others from the majority of scholars. It was also narrated by Ibn al-Mundhir from Abu Bakr as-Siddeeq, ‘Ali ibn Abi Taalib, Ibn Mas‘ood, ‘Ammaar ibn Yaasir, and Naafi‘ ibn ‘Abd al-Haarith (may Allah be pleased with them). It was also narrated from the Taabi‘een ‘Ata’ ibn Abi Rabaah, ‘Alqamah, and Abu ‘Abd ar-Rahmaan as-Sulami; and from ath-Thawri, Ahmad, Ishaaq, Abu Thawr and ashaab ar-ra’y. 

Some scholars said that the worshipper should say one taslim. This was the view of Ibn ‘Umar, Anas, Salamah ibn al-Akwa‘ and ‘Aa’ishah (may Allah be pleased with them), as well as al-Hasan, Ibn Sireen, ‘Umar ibn ‘Abd al-‘Azeez, Maalik and al-Awzaa‘i. Ibn al-Mundhir said: ‘Ammaar ibn Abi ‘Ammaar said: In the mosque of the Ansaar they used to say two taslims and in the mosque of the Muhaajireen they used to say one taslim. Ibn al-Mundhir said: I favour the former. 

Then an-Nawawi said: Our view is that what is obligatory is one taslim, and the second is not obligatory. This was the view of the majority of scholars, or all of them. Ibn al-Mundhir said: The scholars are unanimously agreed that the prayer of one who limits it to one taslim is valid. At-Tahhaawi, al-Qaadi Abu’t-Tayyib and others narrated from al-Hasan ibn Saalih that he regarded both taslims as obligatory. This was also narrated from Ahmad, and was the view of some of the companions of Maalik.

End quote. 

Ibn Qudaamah (may Allah have mercy on him) said: It is prescribed to say two taslims, right and left. 

That is because of the report narrated by Ibn Mas‘ood (may Allah be pleased with him) who said: I saw the Prophet (blessings and peace of Allah be upon him) saying the taslim, (turning his head) until the whiteness of his cheek could be seen, to the right and to the left. It was narrated from Jaabir ibn Samurah (may Allah be pleased with him) that the Prophet (blessings and peace of Allah be upon him) said: “It is sufficient for one of you to place his hand on his thigh, then say salaam to his brother on his right and on his left.” Narrated by Muslim. According to another version of the hadeeth of Ibn Mas‘ood: The Prophet (blessings and peace of Allah be upon him) used to say the taslim to his right: ‘As-salaamu ‘alaykum wa rahmat-Allah’ and to his left: ‘As-salaamu ‘alaykum wa rahmat-Allah.’ At-Tirmidhi said: The hadeeth of Ibn Mas‘ood is a saheeh hasan hadeeth.

End quote from al-Mughni (1/323). 

The view of Imam Maalik, as it says in Mawaahib al-Jaleel (1/526) is that the worshipper should say three taslims: the first to his right, to conclude and exit his prayer, the second, which he should intend as a greeting to the imam, and the third, which he should intend as a greeting to those who are on his left. This view was rejected by al-Qaadi Abu Bakr ibn al-‘Arabi (may Allah have mercy on him), who favoured the view that the second taslim should be intended as a greeting to both the imam and the other worshippers, and the third is a bid‘ah (innovation). He (may Allah have mercy on him) said: He should say two taslims: one to his right which he should intend to conclude and exit the prayer, and the second to his left which he should intend as a greeting to the imam and congregation. The third he should avoid, because it is a bid‘ah (innovation), that was not proven from the Prophet (blessings and peace of Allah be upon him) or the Sahaabah.

End quote from Mawaahib al-Jaleel. 

To sum up: What is encouraged (mustahabb) is for the worshipper to say two taslims, whether he is the imam or praying behind an imam, and if the imam limits it to one taslim, it is encouraged for the worshipper who is praying behind him to say two taslims, one to his right and the second to his left. 

And Allah knows best.