I have hit major problems migrating from live messenger to skype.

My computer is used by more than one person, both with different Live Messenger accounts.

I logged in as user "B", and clicked the "A new version of Messenger is available. Get it now" link. 

This uninstalled Live Messenger, and installed Skype.

Logging into Skype, as User "B" just gets to the page which advises "signed in with a Microsoft Account", and asks "I have a Skype Account"/ I'm New to Skype".  "I have a Skype Account" does not recognise the Microsoft Account, and "I'm new to Skype" responds (After agreeing , "join skype") "Sorry, something went wrong. Please try again".

Logging into Skype, as User "A" logs into  Skype ok, but there are no contacts there.

On another machine, I can log into user "B" using Live Messenger, but not User "A".

Following advice elsewhere, logging on using http://people.live.com, both User "A" & "B" show the contacts, and none "missing".

Inviting an existing (missing) contact on the user "A" account from here sends an email to the missing contact, and following the links to accept the invite on this email works, but the contact still doesn't appear on Skype.

Question 1.  How else can I get the missing contacts which show on   http://people.live.com to appear on Skype.

Question 2. I assume that the "migration" only migrated the first Account which was used on Live Messenger on that computer. How can I migrate the other account(s) to Skype, noting that I no longer have Live Messenger on that machine, and other machines with Live Messenger installed will hit the same problem as they have different other Live Messenger user accounts.