At least once a month I will get a phone call or email message from somebody that would like us to install parts they bought either from an Auto Parts Store or online. I understand you want to save a couple of bucks.
However asking a repair shop to do this is akin to walking into an Outback steakhouse, handing them a T-bone and telling them to cook it for you. Graphic but true. You buy groceries at the grocery store cheaper than if you bought them at a restaurant. Same goes for the auto parts store.
Why is it cheaper? It's cheaper because you are expected to prepare your groceries yourselves. Well it's the same with auto parts. When you purchase an auto part; it is assumed that you know how to install it. Have the tools to install the part, and the skill to install it. Therefore you get the parts cheaper than if you had a repair shop install the parts.
Making a profit on the parts we install on your vehicle is part of the equation of keeping a shop open and running. I have not gone into the logistics of also warranting your parts if it breaks. Who pays? who pays for the labor to replace the part again?
This is why most shops will not install customer supplied parts, and you will have a hard time finding somebody who will. Occasionally we will install customer supplied parts. Mostly because the parts are hard to find and we are working on a specialty car.