Praise be to Allah.
If the loss of the bag was due to heedlessness on the part of the person who you entrusted [with the money to buy the watch], such as if he left it in a place where it was vulnerable to theft, or he did not take care to stand over it in the baggage reclaim area, then he is liable and must pay back to you what you gave him towards the cost of the watch.
If the loss of the watch happened without any negligence on his part, then he is not liable for it, and you must give him the remainder of the money that he paid [for the watch] on your behalf.
The guideline, as the scholars stated, is that an honest person is not liable unless he transgresses or is negligent.
Ibn Qudaamah said in al-Kaafi:
The agent [one appointed to do something on another person’s behalf] is a trustee; he is not liable for the loss or destruction of anything entrusted to his care if he is not negligent, regardless of whether he is being paid for acting an agent or not. End quote.
Shaykh Ibn ‘Uthaymeen said in his commentary on al-Kaafi:
The correct view is that no trustee is liable except in the case of deliberate transgression or negligence. Trustees are all those who take into their care wealth or property with the permission of an Islamic ruling or the permission of the owner. This is the definition of a trustee; it is anyone who has wealth or property in his care with the permission of the Lawgiver, such as the wakeel (guardian) of an orphan, or with the permission of the owner, such as an agent, hired employee, and the like.
End quote from Sharh al-Kaafi (5/125),
For more information, please see the answer to question no. 75568.
Our advice to you is to come to some agreement with your friend with which you are both pleased, such as splitting the cost between the two of you, and the like.
And Allah knows best.