There is some confusion concerning this matter. Some modern scholars were certain that this is permissible, because paper money is something other than silver. Others said that it is haraam, because paper money is currency that is common among people, and it has taken the place of silver, so it comes under the same rulings. As for my own view, at present I am not sure of either opinion, but I think that to be on the safe side it is better not to do that, because the Prophet (peace and blessings of Allaah be upon him) said, “Leave that which makes you doubt for that which does not make you doubt.” And he (peace and blessings of Allaah be upon him) said: “Whoever keeps away from ambiguous matters is protecting his religion and his honour.” And he (peace and blessings of Allaah be upon him) said: “Righteousness is a good attitude and sin is that which makes you uncomfortable and you do not want people to see you doing it.”
So in order to be on the safe side it is better to sell silver coins for something else, such as gold etc, then buy paper money with that. If the one who has paper money wants to buy silver coins he should sell the paper for gold etc., then use that to buy the silver coins he wants.