Transferring Xbox account onto a new Microsoft account.

I have similar issue.
When my son got an Xbox I set him up under my account; he was very young and I didn't want him to have his own account. Seemed best practice to set him up under my account.

He will be 18 this year, he now has a Microsoft account, and wants to have his Xbox account under his own Microsoft account.

It's absolutely ridiculous that Microsoft don't allow transfer between family members to account for kids growing up and wanting to take control of their own digital assets.

Unfortunately that is not possible. Xbox accounts and Microsoft accounts are essentially the same thing. Nothing can be transferred between accounts.

You can transfer it to a new Microsoft Account, you'd need to make the new account at signup.live.com, then go onto your Xbox and go to Settings -> Account -> Account Security. From there there will be a Change Microsoft Account option, follow the steps
there.

If you have a Windows Phone purchases of Windows Phone apps won't carry over to the new account.

You can't. Content can be transferred to new consoles (via license transfer) but they must remain on the account that was used to purchase it. Unless you've gotten your account banned, there's no reason you can't just recover that tag onto the new console.
It's relatively painless.

Alternatively, you could put the account onto a thumb drive and transfer it that way.

Unfortunately they are locked onto that suspended account. It's impossible to transfer the microsoft points into another account.