To remove a product from your inventory/stock list in Phorest, you first need to ensure that the inventory/stock is set to zero items in stock. To do this, click on Manager > Stock/Inventory. 

Select the item you would like to archive and ensure the stock level is set to zero. Click on the blue box to the left of the Brand name. 

From the bottom of the screen, click on the blue Archive button.  

This will remove that item from your Product list. If you would like to put this item back on your Product list, click on the Archived button at the top of the screen. This will display all of the stock/inventory items that you have archived. 

Click on the blue box to the left of the Brand name. From the bottom of the screen, click on the Un-Archive button. This will place that stock item back into your Product list. To see it, untick the Archived button and your current product list will be displayed including the item you just un-archived.