Using an explicit intermediate hash cleans up the code somewhat (for some definition of clean):

use strict;
use warnings;
use Data::Dump::Streamer;

my $allusers = [ {...} ]; # Data per sample
my %users;

for my $user (@$allusers) {
    my $name = $user->{user};

    $users{$name}{$_} += $user->{$_} for qw(duration amount);
}

@$allusers = map {
    {user => $_, duration => $users{$_}{duration}, amount => $users{$_
+}{amount}}
    } sort keys %users;

Dump $allusers;
[download]

Prints:

$ARRAY1 = [
            {
              amount   => 600,
              duration => 6,
              user     => 'Michael'
            },
            {
              amount   => 700,
              duration => 7,
              user     => 'Sarah'
            },
            {
              amount   => 800,
              duration => 8,
              user     => 'William'
            }
          ];
[download]