If PFF could not be cleared it means fault was not rectified. Read the battery with bqStudio to get understanding about safety flags which dont allow to clear all errors. 

Unfortunatelly, my bqStudio doesn't have plugin for BQ40Z556 

I tried to read the battery with BQ40Z50 plugin and got this:

It looks like correct result for PFStatus = 01000000

only 1 bit is set to high - IFC (Instruction Flash Checksum Permanent Failure)

Is it possible to correct this issue?

Posted by: @str

I tried to read the battery with BQ40Z50 plugin

 Correct, bq40z50 could be used to read flags on bq40z556 

Posted by: @str

only 1 bit is set to high - IFC (Instruction Flash Checksum Permanent Failure)

 It is quite rare fault. It means firmware is corrupted or reflashed with another version. Could you describe previous battery history ?.. 

May be it was already repaired before. 

Posted by: @str

Is it possible to correct this issue?

 Yes, by reflashing correct firmware. 

Posted by: @djibattworkshop

Could you describe previous battery history ?.. 

Th battery is new, we sold it to our customer few weeks ago

Now it returned with comment "battery worked for 1 day only, now is not being charged and laptop doesn't power on without ac adapter".

So, nobody repaired it.

Posted by: @djibattworkshop

Yes, by reflashing correct firmware. 

I've never did this before.

Does it mean to read FW from any (?) working battery with BQ40Z556 chip which has V0.08 firmware and write it to this battery using bqStudio?

The easiest way is to copy SREC from same new but working battery and reflash subject battery. 

SREC contains all necessary binaries like IF, IFIB and EEPROM. 

Another option is to reflash IF only but it is not trivial task for beginners. 

Many thanks to @djibattworkshop - I did it

I don't have working B31N1736 at the moment, so I took another Asus battery with the same firmware (B41N1711)

Compared IF section of both SREC files, and found out the difference in 3 bytes only.

Changed these 3 bytes, wrote corrected firmware to B31N1736, cleared chip errors again and everything works now

Good job done ! 

Posted by: @djibattworkshop

The easiest way is to copy SREC from same new but working battery and reflash subject battery. 

SREC contains all necessary binaries like IF, IFIB and EEPROM. 

what does SERC, IF, IFIB stands for? how they are read, by BQStudio?

SREC - Motorola S-Record encoded binary 

https://en.m.wikipedia.org/wiki/SREC_(file_format)  

SENC - Srec ENCrypted 

IF - Instruction Flash 

IFIB - Instruction Flash Information Block 

OTP - One-time Programmable Memory 

ROM - Read-Only Memory 

EEPROM - Electrically Erasable Programmable ROM 

Posted by: @brs

how they are read, by BQStudio?

SREC - by bqStudio 

SENC - by bqEVSW 

EEPROM - by NLBA1 

IF, IFIB - by engineering tools