SOLVED: Does Skype For Business on Office 365 Connect to Standard Skype

The short answer is yes, but you need to add each contact one by one using their Skype Name  2015.

In April 2015, Microsoft Offce365 support said:

…it is not feasible to add the free Skype users except those who have Microsoft accounts as contacts to Skype for Business.

Currently, to use the Skype directory integration feature, a Skype for Business Server 2015 is required in the backend server. Due to that currently the backend servers haven’t upgraded yet, the feature is still not available in Office 365 Online. For more details, please refer to the feature instructions about Skype directory integration in: https://support.office.com/en-us/article/Lync-is-now-Skype-for-Business-%E2%80%94-see-whats-new-aba02d7e-c801-4a82-bccd-e7207240f612?ui=en-US&rs=en-US.

https://community.office365.com/en-us/f/166/t/346441

but this has now changed.  Also remember:

1. If you have your own Lync 2010 or newer backend server (i.e. NOT Office 365) you can configure it to allow hooks into the standard free Skype systems.
2. Also, remember that Skype For Business and Skype are, in 2015, completely separate applications so you can run both of them at the same time.

It is frustrating that there is no ready way to merge a standard free Skype and a Skype For Business (SFB) account, but that is the way it is.

There is an active Skype For Business to Skype thread available on Skype support: http://community.skype.com/t5/Using-Skype-in-your-business/Combining-Skype-and-Skype-for-business-accounts/td-p/3954928/page/5