Microsoft only bought the handset business from Nokia, they didn't purchase all of Nokia. In fact, as I recall, they only got the right to use some of the brand names for a limited period of time.
Right, that makes sense! And the Alcatel that Nokia is buying here, is much more than a producer of phones.
Actually the Alcatel-Lucent they bought do not produce phones at all ;)
A while ago Alcatel got with TCL, a Chinese company, to take care of the handset business through a joint-venture initially. Then TCL bought and integrated the JV, and kept the rights to the Alcatel brand for handsets. The brand is likely to stay but it's now fully TCL (with still some ex-Alcatel employees).