To open a filehandle once the easiest way would be to have one central function for opening a file that caches the filehandle:

my %filehandles;
sub open_file {
    my( $filename ) = @_;
    if( ! $filehandles{ $filename }) {
        open $filehandles{ $filename }, '>>', $filename
            or die "Couldn't append to '$filename': $!";
    };
    return $filehandles{ $filename }
}

...

my $fh = open_file( 'path1' );
print $fh "Hello\n";
my $fh2 = open_file( 'path1' );
print $fh2 "world!\n";
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As for your programming style, you are launching external processes several times to retrieve information. This can lead to inconsistent errors if a service comes up or goes down between your two queries. Better retrieve the information one into an array. Also, don't use an external grep command when Perl has a built-in grep:

my @services = `systemctl list-unit-files`;
if( my @smb = grep { /smb\.service/ } @services ) {
    my $fh = open_file( 'path1' );
    print DATEI "chkconfig smb: OK\n";
    print DATEI "Output:_\n " . join( "", @smb) . \n\n;
};
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Update: The return statement in the function was wrong. Spotted by soonix++