Is there a way to find out information on battery through macbook serial number? i bought my MBP Retina display 13"(late 2013) 5 months ago; a week ago i had to change its battery at an authorised reseller when my small sister accidentally dropped a whole glass of water on it.
i think my new battery isn't the same as the one i had before.
i paid a LOT of money to get it fixed...
my question is: is there any way i can find out my old battery's information and/or serial # through my MBP's serial number?
or if anyone has the same mac model would you be kind enough to share your battery(original) information? 

MacBook Information: MacBook Pro Core i5 2.6 13" Retina Late 2013 

Current Battery Information: 

Model Information:

Serial Number:

Manufacturer: SMP

Device Name:  bq20z45  (i researched and there should be a 1 after the 5)

Pack Lot Code:    0

PCB Lot Code: 0

Firmware Version: 702

Hardware Revision:    3

Cell Revision:    379

Charge Information:

Charge Remaining (mAh):   3870

Fully Charged:    No

Charging: No

Full Charge Capacity (mAh): 6211  (I believe this should be around 8000)

Health Information:

Cycle Count:  3

Condition:    Normal

Battery Installed:    Yes

Amperage (mA):    -485

Voltage (mV): 11772

Any information is much appreciated :)
Unfortunately, information would not be attainable simply through the serial number. It is unlikely that you obtained the incorrect battery, since AASP's source their parts from Apple to perform warranty-service repairs. I poked around online and noted that you are not the only one who has the bq20z45 part number from SMP, nor the only one to have a Full Charge Capacity different than ~8000. I found this via various user screenshots on Amazon. 

Likely, the battery is correct for your unit and will function as expected. If not, all warranty repair services are either covered by your Applecare Protection Plan or, if out of warranty, 90 days from date of service. Should you continue to have concerns, I'd call the AASP back to verify that you got the right item.

EDIT: It may be worth it for you to calibrate your battery. Charge all the way to 100%, then unplug the unit and use it until it dies w/o charging it up again. Repeat once and that should get your battery reporting accurately as well.