Is it permissible to make use of some forgotten items left by their owner in the shop for more than a year, for which he has not come to inquire, after giving some of them in charity?

If the lost item is insignificant and its owner would not pursue it, then there is no harm in benefiting from it. However, if it has value and its owner would pursue it, then the finder must announce it for a year. If he intentionally fails to do so, he has sinned, and he must announce it now, unless he believes that the owner is unlikely to be identified. Since the questioner donated some of it and took some, he is liable if the owner ever appears. He may benefit from what remains, with the condition of his liability.

If he knows the owner of the items and found them in the shop, then it is a trust that he must keep until its owner returns. If he despairs of the owner's return, he should give it as charity on the owner's behalf. Therefore, he must give as charity what remains with him after despairing of the owner's return, and give as charity the value of what he consumed.