Migrate from Iceweasel to Firefox on Debian Jessie

[commentsabout at riseup.net]

Hello,

I used to get my Iceweasel updates from http://mozilla.debian.net.

I noticed a couple of weeks ago that I didn't received updates anymore 
[1] (I'm currently running Iceweasel 44.0.2) and stumbled upon the 
announcement about the fact that the issues related to the Firefox 
branding are now fixed and therefore Firefox will be integrated as of 
now. That's great news :)

How do I migrate from Iceweasel to Firefox without losing all my stuff 
(profile, extensions, history,...) ?

Thank you in advance for you help.

Best,

CA

[1] W: Failed to fetch 
http://mozilla.debian.net/dists/jessie-backports/Release  Unable to find 
expected entry 'iceweasel-release/binary-amd64/Packages' in Release file 
(Wrong sources.list entry or malformed file)