Is it permissible to donate the value of a lost trust (a watch) as compensation to its owner, with whom communication has become impossible?

If the watch was lost without negligence on your part, then you are not liable for it, and you are not required to return its value. However, if it was lost due to your negligence, then you are liable for it and must pay its value to its owner. It is not sufficient to give its value in charity as long as returning it is possible. Furthermore, estrangement and abandonment between Muslims are forbidden in Islamic law.