[Samsung Galaxy Nexus] Finnbaerle:
Quick Fix via microSD

I've come up with another solution. You need a huge microSD card plus the environment set up according to the manual in the topic header (but you could just use a rooted Android device and terminal emulator instead of PC with cygwin just as well).

0. Proceed to the original instruction in the topic header, complete steps 1-4.

1. At the step 5 use instead:

adb shell

2. Find out which Android partition you need to recover by entering

ls -l /dev/block/platform/msm_sdcc.1/by-name/

In my case (SGS4 GT-I9505) it was:

$ adb shell
shell@jflte:/ $ ls -l /dev/block/platform/msm_sdcc.1/by-name/
ls -l /dev/block/platform/msm_sdcc.1/by-name/
lrwxrwxrwx root root 2014-04-20 21:43 aboot -> /dev/block/mmcblk0p6
lrwxrwxrwx root root 2014-04-20 21:43 apnhlos -> /dev/block/mmcblk0p1
lrwxrwxrwx root root 2014-04-20 21:43 backup -> /dev/block/mmcblk0p23
lrwxrwxrwx root root 2014-04-20 21:43 boot -> /dev/block/mmcblk0p20
lrwxrwxrwx root root 2014-04-20 21:43 cache -> /dev/block/mmcblk0p18
lrwxrwxrwx root root 2014-04-20 21:43 carrier -> /dev/block/mmcblk0p28
lrwxrwxrwx root root 2014-04-20 21:43 efs -> /dev/block/mmcblk0p10
lrwxrwxrwx root root 2014-04-20 21:43 fota -> /dev/block/mmcblk0p22
lrwxrwxrwx root root 2014-04-20 21:43 fsg -> /dev/block/mmcblk0p24
lrwxrwxrwx root root 2014-04-20 21:43 hidden -> /dev/block/mmcblk0p27
lrwxrwxrwx root root 2014-04-20 21:43 m9kefs1 -> /dev/block/mmcblk0p13
lrwxrwxrwx root root 2014-04-20 21:43 m9kefs2 -> /dev/block/mmcblk0p14
lrwxrwxrwx root root 2014-04-20 21:43 m9kefs3 -> /dev/block/mmcblk0p15
lrwxrwxrwx root root 2014-04-20 21:43 mdm -> /dev/block/mmcblk0p2
lrwxrwxrwx root root 2014-04-20 21:43 modemst1 -> /dev/block/mmcblk0p11
lrwxrwxrwx root root 2014-04-20 21:43 modemst2 -> /dev/block/mmcblk0p12
lrwxrwxrwx root root 2014-04-20 21:43 pad -> /dev/block/mmcblk0p9
lrwxrwxrwx root root 2014-04-20 21:43 param -> /dev/block/mmcblk0p19
lrwxrwxrwx root root 2014-04-20 21:43 persdata -> /dev/block/mmcblk0p26
lrwxrwxrwx root root 2014-04-20 21:43 persist -> /dev/block/mmcblk0p17
lrwxrwxrwx root root 2014-04-20 21:43 recovery -> /dev/block/mmcblk0p21
lrwxrwxrwx root root 2014-04-20 21:43 rpm -> /dev/block/mmcblk0p7
lrwxrwxrwx root root 2014-04-20 21:43 sbl1 -> /dev/block/mmcblk0p3
lrwxrwxrwx root root 2014-04-20 21:43 sbl2 -> /dev/block/mmcblk0p4
lrwxrwxrwx root root 2014-04-20 21:43 sbl3 -> /dev/block/mmcblk0p5
lrwxrwxrwx root root 2014-04-20 21:43 ssd -> /dev/block/mmcblk0p25
lrwxrwxrwx root root 2014-04-20 21:43 system -> /dev/block/mmcblk0p16
lrwxrwxrwx root root 2014-04-20 21:43 tz -> /dev/block/mmcblk0p8
lrwxrwxrwx root root 2014-04-20 21:43 userdata -> /dev/block/mmcblk0p29

So that I needed /dev/block/mmcblk0p29 for userdata.

3. So then you just perform a blockwise backup of userdata to your extSD:

$ adb shell su -c dd if=/dev/block/mmcblk0p29 of=/storage/extSdCard/userdata.img
19456000+0 records in
19456000+0 records out
9961472000 bytes transferred in 771.191 secs (12916997 bytes/sec)

4. Proceed to steps 8-23, and take care!

P.S. I figured out, in order to keep the original Ext4 structure of exported partition I would rather not convert the raw file into anything like vhd. I would use R-Studio feeding it the raw image itself.