In Othello, who finds the handkerchief when Desdemona loses it?

The handkerchief in Othello is one of
the most famous props in all of Shakespeare.  So, it's comings and goings, tracked by
way of stage directions, are very important to the plot of the
play.

In Act III, scene iii, my
Arden edition of the text gives the stage direction as "She drops her
handkerchief," after Othello's line "Your napkin is too little."  Almost immediately,
Desdemona and Othello exit, and Emilia, alone onstage, picks it up.  She
says:

I am
glad I have found this napkin. . .

My wayward husband hath
a hundred times

Woo'd me to steal it. .
.

Iago enters and manages to
take it, apparently against Emilia wishes, who says:

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Give me 't again, poor lady, she'll run
mad

When she shall lack
it.

But the deed is done. 
The handkerchief is in the hands of Iago and will become a key prop in his further
insistence to Othello that his wife is being unfaithful with
Cassio.