Seems that avrdude recognizes the board:
Block Poll Page Polled
Memory Type Mode Delay Size Indx Paged Size Size #Pages MinW MaxW ReadBack
----------- ---- ----- ----- ---- ------ ------ ---- ------ ----- ----- ---------
eeprom 65 20 4 0 no 1024 4 0 3600 3600 0xff 0xff
flash 65 6 128 0 yes 32768 128 256 4500 4500 0xff 0xff
lfuse 0 0 0 0 no 1 0 0 4500 4500 0x00 0x00
hfuse 0 0 0 0 no 1 0 0 4500 4500 0x00 0x00
efuse 0 0 0 0 no 1 0 0 4500 4500 0x00 0x00
lock 0 0 0 0 no 1 0 0 4500 4500 0x00 0x00
calibration 0 0 0 0 no 1 0 0 0 0 0x00 0x00
signature 0 0 0 0 no 3 0 0 0 0 0x00 0x00
P.S. I have tried 3 different USB cables, all of them work correctly (board is detected by Windows and IDE) and with 1 of them I had writing process completed.