Hi friends,
Have a lot of posts because this problem with module mail alert (prestashop official), about as show only product out of stock:
Insert this code in line 450 more or less:
<!-- Out of stock hook -->
{if (!$allow_oosp && $product->quantity <= 0) OR !$product->available_for_order OR (isset($restricted_country_mode) AND $restricted_country_mode) OR $PS_CATALOG_MODE}
<div id="oosHook"{if $product->quantity > 0} style="display: none;"{/if}>
</div>
{$HOOK_PRODUCT_OOS}
{/if}
I use prestashop 1.6.0.9