How to upgrade 1511 from Home to Pro?

If you're correctly booting the media (as a UEFI device if offered) to delete all partitions and then click next to auto-format, then it should ask which version you want.  The exception is if it sees an embedded Windows 8/8.1 Home Product Key it will force Home.

If you also used the latest bootable media for Version 1803 created from Media Creation Tool, then it should allow using thePro key to do the Easy Upgrade from Activation Settings.  For older versions it requires first inserting the Pro Generic key to install Windows 10 RTM to change to Pro, then activating with your Pro Product Key. 

If you reinstalled an older version then I'd not mess with the buggy Windows Update assistant but reinstall with the latest media  following the illustrated steps in this link which compile the best possible Clean Install of Windows which will stay that way as long as you stick with the tools and methods given, has zero reported problems, and is better than any amount of money could buy:   Clean Install Windows 10

I'm not having any luck figuring out how to upgrade from Home to Pro with an existing key.  My system has been running Home and is currently running version 1511.  I've decided to go ahead and use an existing key to upgrade to Pro.  I did a clean install, expecting to be asked to specify a version and provide a key during install, but was never asked for either.  The installer simply formatted the hard drive and installed Home and activated it, with no input from me after the install started other than agree to the terms and tell it my language.

OK, no problem I thought, I'll just go to the Activation setting and give it the new key from there.  However, if I tell it I want to change the key it comes back and says the key I'm giving it can only activate Pro and I'm running Home.  If I go the Store route and tell it I already have a Pro key, it gives me the same message - it tells me my key is for Pro but I'm running Home.  Nowhere along the way does it offer to take my key and give me the upgrade, rather it implies that I must somehow magically upgrade it myself before changing the key.  And that would be fine if I could figure out how to do that.

Anyone know how to force an install of Pro when the installer automatically installs Home with no option given to change it?

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You can temporarily use Team Viewer if possible, since it works much better anyway. 

We had been told by Support manager that the V.1703 would limit the ability to change to Pro version with the default key to only those who already have the Pro Digital License assigned to the PC.  Did you?

If so using a Pro Product Key should work.  That it doesn't needs attention from Support to either get it fixed or know why not. 

I'd use chat here:  https://partner.support.services.microsoft.com/en-us/contact/menu/software/windows/setup/

Please observe what they do or ask them specifically so you can report it back here to help others.