You can install your Photoshop Elements 2019 product on up to two computers. If you want to move your product to a new computer, simply choose Help > Sign Out in the product from one of the computers that has an active licence. You can then install the product on your new computer.
You can download the software to your Windows laptop from the link below. Licence with your serial number after installation. If you also wish to continue using PSE 2019 on your desktop, stay signed-in.