If there is more than one user, I would take that a few steps further. Don't give the user rights to download, instead download the installer yourself using Mark's instructions. Download any SPs, hotfixes, and plug-ins as well. Back all of those up somewhere along with serial numbers, product codes, and reseller contact info.
Using the installer, build a deployment on the network using the appropriate license type (Desktop, network). Most, if not all, users should have read-only rights to that location. When a user needs a specific program you can either point them to the shortcut created by the deployment creator OR use management software like SCCM to "push" the install to the users computer without needing their input.
Easy-peasy. Only need to download once, less work for IT, less work for users, safe from critical failures like computer failure, fire, or the manager getting hit by a bus, and you still have a copy of that installer in case it gets retired later.
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If you are going to fly by the seat of your pants, expect friction burns.
"I don't know" is the beginning of knowledge, not the end.