> $h{k2}=FH

will only work in no strict scenarios, here corrected versions

use v5.12;
use warnings;
use Data::Dump;


my %h;

open my $fh, ">>", \ my $out;
$h{k}=$fh;
$h{k}->print("bla");
dd $out;


open FH2, ">>", \ my $out2;
$h{k2}=*FH2;
$h{k2}->print("bla2");
dd $out2;


open FH3, ">>", \ my $out3;
$h{k3}=\*FH3;
$h{k3}->print("bla3");
dd $out3;


# open FH4, ">>", \ my $out4;
# $h{k4}=FH4;
# $h{k4}->print("bla4");
# dd $out4;

# Bareword "FH4" not allowed while "strict subs" in use at c:/tmp/pm/f
+h.pl line 27.
# Execution of c:/tmp/pm/fh.pl aborted due to compilation errors.
[download]

    
"bla"
"bla2"
"bla3"
[download]

FWIW: I prefer the 3rd $h{k3}=\*FH3 over the 2nd variant