Hi, if the HP has both a graphics card and integrated HD 6530D then you can move the graphics card to the Dell assuming it fits. If it only has "integrated" that mean the video is in the CPU chip, and you can't remove it. There are two sizes for graphics cards, one is called 'low profile' and is shorter than the other. If your HP is a low profile system then the card won't fit.
When you go to remove the card from the HP there is an obvious system that hold the card to the case on the end of the card where you plug in the video cable. Typically you undo this first. There is a much less obvious catch at the end of the PCIe slot farthest from where you plug the video cable. Using your finger to push the catch you lift the card straight up. If the card will not go straight up then the catch is not properly released. You do not need to yank teh card hard to get it loose, that won't work adn could break the MB.
gl