To search for a product with its short form name, please add an item custom field 1st and add the short form in the created custom field.
Step 1: Please check the steps from the link to know how to add a custom field for an item.
Step 2: After adding a custom field, enter the short name of the product in that field.
Step 3: While creating the invoice, search using the short name of the product to quickly find and select it.