Corrected entry: When Lucy gives Tumnus the handkerchief, Tumnnus gives it to the Beaver just before he gets captured by the White Witch. The Beaver then gives the handkerchief to Lucy, then right at the end when Tumnus has been revived by Aslan, Tumnus has the handkerchief and gives it to Lucy.
Correction: This is not the same handkerchief. The one Beaver had given to Lucy was, of course, Lucy's, but the one which Tumnus gave her at the end was his own one. This is a kind of payback.