I was in this exact situation last month when sorting parts for my home server, and I was so happy when I figured out this workaround. It works well and saves a ton of time. While you cant directly merge carts, using a Wish List is super easy and I have no complaints with how it turned out. Here is what you need to do:

• Go to your work cart and select Move to Wish List for each of the items.
• Make that Wish List public or shared in the list settings.
• Copy the share link and email it to yourself or open it in your personal browser.
• Log into your personal Prime account, open the link, and you can add them all to your cart from there. Its not a single click but it beats searching for 15 different PC parts again. Let me know if you get stuck on any of the steps.

^ This. Also, in my experience, check the prices again before you buy on the Prime account. Amazon prices fluctuate constantly, and sometimes work account discounts actually beat Prime deals. I always check because even a 5% difference on a $500 build adds up. If the prices are the same, just use the registry trick to move them.

Just seeing this now. Are you buying all these parts at once, or do you need them split for tax purposes? Over the years I've found a couple technical workarounds for this:

• Use a bulk ASIN grabber tool to copy-paste the product IDs
• Convert the cart to a registry for a one-click transfer I actually found a solution on Share-A-Cart that works perfectly for sharing Amazon lists without giving out your password.