All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger.
There is no religious impediment to sending the Salaam to someone with someone else. Al-Bukhaari allocated a chapter in his book Saheeh Al-Bukhaari entitled, "Chapter: If one says, 'So-and-so sends the Salaam to you.'" He cited the following hadeeth therein: ‘Aa'ishah, may Allah be pleased with him, reported that the Prophet, sallallahu ‘alayhi wa sallam, said to her, "Jibreel (Gabriel) sends the Salaam to you." So she said, "Wa ‘alayhi As-Salaam Wa Rahmatullah (which means: And upon him is peace and mercy of Allah)."
It was also reported that the Prophet, sallallahu ‘alayhi wa sallam, asked some of his Companions to convey his greetings of peace to others, as in the hadeeth in which Anas ibn Maalik, may Allah be pleased with him, said, "A young man from Aslam said, 'O Messenger of Allah, I wish to join a military expedition, but I have nothing to equip myself with.' He, sallallahu ‘alayhi wa sallam, said, 'Go to so-and-so, for he had prepared himself (for battle), but he fell ill, and tell him that the Messenger of Allah, sallallahu ‘alayhi wa sallam, sends him Salaam and says, ‘Give me what you had prepared for battle...’'" [Muslim]
The person entrusted with conveying the greetings bears no sin if he forgets to convey them, as a person shall not be held accountable for what he did out of forgetfulness. The Prophet, sallallahu ‘alayhi wa sallam, said, "Verily, Allah has pardoned for my nation their mistakes, forgetfulness, and that which they have been forced to do under duress." [Ahmad and others]
The scholars held different views as to whether the person is obliged to convey the greeting or not. Al-Haafith Ibn Hajar wrote in his commentary on the previously cited hadeeth (narrated by ‘Aa'ishah, may Allah be pleased with her):
"An-Nawawi said, 'It is deduced from this hadeeth that it is prescribed to send the Salaam to someone and that the messenger (the person entrusted with conveying the greetings) is obliged to convey it because it is a trust; but some said that it is similar to a deposit. The correct view in this regard is that if the messenger accepts this duty and agrees to convey the Salaam, it becomes like a trust (a binding commitment), otherwise it is like a deposit; in case the deposit is not accepted, there is no binding commitment. It is also deduced from the hadeeth that when someone conveys the Salaam from another person verbally or in a written form, it is recommended for the greeted person to return the Salaam immediately. It is recommended to return the Salaam to the one conveying it as well. It was reported that a man from the tribe of Tameem conveyed to the Messenger of Allah, sallallahu ‘alayhi wa sallam, greetings of peace from his father, so he, sallallahu ‘alayhi wa sallam, said to him, ‘And upon you and upon your father be peace.’ [An-Nasaa'i] We have previously underlined in the merits of Khadeejah that when the Prophet, sallallahu ‘alayhi wa sallam, informed her that Jibreel conveyed the greetings of peace (Salaam) from Allah to her, she said, ‘Indeed, Allah is Peace and from Him is peace; and upon you and upon Jibreel be peace.’'"
Allah knows best.