It all depends.
What tournament where when?
Who ran it?
What rules were being used.
FIDE would require signing the score sheet.
Shaking hands means nothing except you like spreading germs around.
If he kept playing on after she did that would pretty much prove it was not mate and overrule any claims that she resigned.
Your kid should refer to
21F3. Facts are not agreed upon.
If the facts are not agreed upon, the director should proceed as follows:a. A director who is satisfied that the facts have been ascertained should rule accordingly.
b. A director who is unable to satisfactorily determine the facts must make a ruling that will permit play to continue.
See also 1C2, Director discretion;
say the facts are not agreed on. Use the position on the board as proof. and ask also for a ruling on the facts and also if needed IC2 Director discretion.
Especially since this is a kiddie tournament the TD should not award the win even if there was a meaningless handshake to the person who made an erroneous claim.
Depending on other factors they might caution the claimant against making claims so as to win improperly and to let the other person realize that it is actually or else move as in this case when it was not mate.
Situations like this emphasize the need to know ALL the rules if one is going to play in a tournament. Some groups may modify the rules or elaborate on them.