Here's a handy guide covering how to get PS4 game updates on a jailbroken 4.05 OFW or 4.55 OFW console from PlayStation 4 developer @MODDEDWARFARE on his YouTube Channel via Twitter. 
This comes following a related tutorial on Adding PS4 Game Updates in Packages (PKGs) for those who missed it.
From the video's description, to quote: How to Get Game Updates on a 4.05/4.55 PS4 (4.05/4.55 Jailbreak)
How to update your games on a 4.05 or 4.55 Jailbroken PS4.
This method is for official games only! It will not work with game backups, only the original disc games.
Update Sites:
Download links:
How To Merge PKGs & Update Games For 4.05 & 4.55 (PS4 Jailbreak)
How to install update PKG files for your PS4 Disc based games using PS4 PKG Update Database! by NagatoRevenge
This comes following a related tutorial on Adding PS4 Game Updates in Packages (PKGs) for those who missed it.
From the video's description, to quote: How to Get Game Updates on a 4.05/4.55 PS4 (4.05/4.55 Jailbreak)
How to update your games on a 4.05 or 4.55 Jailbroken PS4.

Update Sites:
Download links:
How to install update PKG files for your PS4 Disc based games using PS4 PKG Update Database! by NagatoRevenge