Once you are in FAB go to the “My Library” tab at the top of the page. On the asset page you are looking at in FAB, it should have a “Download” button for the item rather than a “Buy Now” button if it is already available to your account. Once you click the “Download” button it will make that asset available to use in your project, but you will then need to go into your Epic Games Launcher, and select Unreal Engine Tab on the left. Then click on Library at the top and it will display 3 sections below. First is the version of your Engines installed, next will be your projects, and last will be your Asset library that is downloaded. You may need to expand these sections to see all items. If you select the project you wish to inject an asset to, you can then click on the “Add to Project” next to each asset you wish to use. Please be aware that for some assets your project may need to be closed then restarted to allow the asset to be available for use after injecting it.
I hope this information is clear and helpful in some way.