DV6 6170sl screen upgrade, HD to FHD display (some clarification and advice))

Hi guys, I wanted to breathe some new life into my old and faithful pc, a 2011 hp dv6 6170SL
I just replaced the hdd with an ssd and I was looking forward to replace the current HD screen with a FHD panel. Needless to say I am a bit confused reguarding original parts, compatible parts, and whether they would be supported by the motherboard/BIOS of my pc model.

I was wondering if somebody with clearer ideas could give me some much needed advice and guidance

This is the maintenance guide of my PC
http://h10032.www1.hp.com/ctg/Manual/c02842252

The new parts to should be
Display 653378-001
FHD Cable 656805-001

All the specs in case they're useful
HP - Pavilion dv6-6170sl Metal Steel Gray
Intel Core i7-2630QM 2.00-GHz (SC turbo up to 2.90-GHz) processor (6.0-MB L3 cache, quad core, 45 W)
RAM 8192MB (2 x 4096MBD DR3)
Hard Disk 500GB (7200RPM)
ATI RADEON HD6770 (2GB GDDR5)
Display 15.6" HD LED BV (1366x768)
DVD Super Multi DL, Wifi b/g/n, LAN Gigabit Ethernet, Intel Wireless Display
2 x USB 3.0 + 2 x USB 2.0, HDMI, digital media card reader, Webcam HD HP TrueVision, TouchPad with Multi-Touch Support,
BEATS AUDIO, HP CoolSense, Fingerprint Reader, HP SimplePass

what I would need to buy:
screen
https://www.laptopscreen.com/Italian/model/HP-Compaq/653378-001/
cable
https://it.aliexpress.com/item/32805340369.html
or
https://www.ebay.it/itm/Cavo-Flat-v...588717?hash=item443583886d:g:ZLcAAOSwwIZXTBok


I guess the most important thing is... does the motherboard and bios of my PC support a FHD Panel? (it would seem so from the maintenance guide, can anybody more knowledgeable than me confirm? )

And for the same value, is there a better quality screen that isn't the display of HP Part Number 653378-001? I read about LG LP156WF1 or AUO B156HW0x (from the post http://forum.notebookreview.com/threads/hp-dv6t-display-replacement.610177/ )

Thank you, I know the laptop is a bit old but any help is appreciated
and feel free to say if the upgrade is worth it or not

 

UPDATE: I ended up upgrading the screen and as of now everything seems to be working well

I'll post what I bought in case somebody needs it
I bought the cable for 10 euros
https://www.ebay.it/itm/Cavo-Flat-v...588717?hash=item443583886d:g:ZLcAAOSwwIZXTBok
(even if the cable that i received was labeled 50.4RN10.012, not 50.4RN10.002 as said on ebay... but it worked so ¯\_(ツ)_/¯ )

The cable wasn't exactly like the original one: the parts where it splits are off by 1 cm or 1,5 cm, the cable for the webcam was a little too long and I had to move the ground loop of about 2 cm to make it closer to the screw (near the display hinges)

I ordered the screen from LCDshop.it, Au Optronics B156Hw01 V.4 (which is matte)
https://www.lcdshop.it/au-optronics...56fh226.html?search=Au Optronics B156Hw01 V.4
It was my understanding that the display would have been an AUO but it arrived labeled as LP156WF1(TL)(F3) (and it was only a compatible display...). Nevertheless the price was ok and I was satisfied with it, so ¯\_(ツ)_/¯