As you recognised, you first need to convert the string "1" to the actual 8-byte big-endian integer.

my $eight_bytes = pack 'Q>', $user_id;
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You can use unpack to get the hex representation back to verify it's correct:

my $hex = unpack 'H16', $eight_bytes;
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Update: renamed $int to $eight_bytes as the value is not an integer in Perl's sense.