Since you are saying that your store is only a multi-store, so I don't think you will see a "
Websites" tab, in that product's details page. So, you have only one way to make this product enabled in "
Shop A" & disabled in "
In the product's details page, Magento loads the "
General" tab, in which you will see the "
Now, in the left side, above the "
General" tab, you will find a dropdown field for "
Choose Store View:". If you click on the dropdown, you will see a list of all your store views available under each Website & Store.
Now select the "
Shop B" in that dropdown. Magento will ask you that it will erase any unsaved data from the current view in Admin, if you have changed any data, without saving it. Without worrying on this part, click the "
OK" button of that dialog box, & Magento will then load the "
Shop B" store view of that same product.
Here beside the "
Status" field, you will find a checkbox. Make sure that it's not checked. Now change the value of the "
Status" dropdown to "
Disabled" & save the changes.
Now go to the front-end of your "
Shop B" store view & you shouldn't be able to see this product again. But it will also be active in the "
Shop A" store view.
Hope it helps.