I think you want +() or {}, but not +{}. With +{}, you will get one hashref per element – whereas I think you want a single hash, in which case you want either an expression (+()) or a single-expression block ({}). But I can only guess.

Other than that confusion, your map is fine, if a little hard to read. I’d put the month extraction code in a subroutine so I could give it a descriptive name. Rather than:

my @mapped_prizes = map +{ $month{(split(/-| /,$_->{'Timestamp'}))[1]}
+ => $_ },  @prizes;
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I’d write:

sub month_from_datetime {
    my ( $datetime ) = @_;
    ( split m{-| }, $datetime )[1]
}

my %month_name = (
    # ...
);

my %mapped_prizes = map {
    my $month_num = month_from_datetime $_->{'Timestamp'};
    $month_name{ $month_num } => $_;
}, @prizes;
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which makes it quite obvious what’s going on.

Makeshifts last the longest.