[Nexus]

М.б. так?

function brifPage() {
    $('#brief').submit(function(e) {
        if (!window.FormData)
            return alert('Class FormData unsupported');

        e.preventDefault();

        var $this = $(this);
        $.ajax({
            type: "POST",
            url: '/ajax/brif.php?brif',
            processData: false,
            contentType: false,
            data: new FormData(this),
            success: function(suc) {
                $('.feedbackThank').fadeIn();
                setTimeout(() => {
                    $('.feedbackThank').fadeOut();
                }, 3000)
                $this.trigger('reset');
            }
        });

    });
}