BQ24735: Power IC CHIP different code/number? Please help

Hi,*

I'm grateful to find such forum and such skilled people.
This might be the stupid thing I've ever asked but I've got to ask to understand.
I've searched myself and I dont believe this will cause any problems.

I've had my laptop defective now for a long time. Today I understood that the charging problem is 
from this preticular chip (BQ735) according to the photos I've taken. 
When laptop is connected to Power Adapter it does not charge the battery or start up (even if battery is removed).
So the problem is from the chip. That I understand from today.

I've already ordered two types of this chip from both Ti Store and Ebay (TI chips and not some China stuff).

The only thing I dont understand at this moment is... On the photos and the chip it says:
BQ375
TI 5BI (or 58I?) and then A8F3 (A8F8?)

Does this mean anything or is it important for me to find exactly this chip number?
Because I've searched the internet and believe me I've searched in every way possible without finding this number/chip model except for BQ24735 TI and even without the 5BI or 58I or even 58K A8F8 or A8F3 etc...

The items I ordered is BQ24735RGRR and BQ24735RGRT
And I even wonder what is the difference between them both? (Another stupid question)..

Thank you for all your help.

Pictures (shared album, Google Photos): photos.app.goo.gl/GYdZnwJ4jPDCnKj86

Best regards