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I think that the potencial problem could be in your sql. I would modify query like as
(added DISTINCT and removed ps_cart_product join)

 $sql = 'SELECT DISTINCT c.id_cart, c.id_lang, cu.id_customer, c.id_shop, cu.firstname, cu.lastname, cu.email, ad.phone_mobile
        FROM '._DB_PREFIX_.'cart c
        LEFT JOIN '._DB_PREFIX_.'orders o ON (o.id_cart = c.id_cart)
        LEFT JOIN '._DB_PREFIX_.'order_history oh ON (oh.id_order = o.id_order)
		LEFT JOIN '._DB_PREFIX_.'address ad ON (c.id_customer = ad.id_customer)
        RIGHT JOIN '._DB_PREFIX_.'customer cu ON (cu.id_customer = c.id_customer)
//        RIGHT JOIN '._DB_PREFIX_.'cart_product cp ON (cp.id_cart = c.id_cart) 
//        Why?? cp is not used in SELECT neither in WHERE
            WHERE DATE_SUB(CURDATE(),INTERVAL 90 DAY) <= c.date_add
            AND o.valid = 0
            AND oh.id_order_state = "6"
            AND cu.newsletter = 1';