Is there a way to update h5p plugin manually?

Hello! 

I am running a wordpress site with h5p plugin on it. 

Wordpress version is 4.9.3, h5p plugin version is 1.10.0

I really want to update a plugin because recent versions has so many useful stuff, but somehow I can't figure out how to update plugin manually. WP is not suggesting me to update plugin and also there is no button "update" in the "add new plugin" form

I've tried to do it manually so I replaced old folder with the new version (1.13.1 I believe) folder, content types stopped to load properly (I believe there are some libraries conflicts with the new version). I've also made a backup of plugin folder and installed new version from "add new plugin" form, it installed properly, but nothing changed actually and content types also crashed. The weird thing is that I've tried to upload Math Library (the main reason I really want to update plugin) manually and it always says that version of h5p core is 1.4 (even then there are lines (1870,1871) in h5p.classes.php file which say that current version is 1.20). At first I've tried to upload math library in "h5p_libraries" tab but after clicking "upload" button the page was just updating and nothing happened (even no warning or error messages)

I'm actually kind of afraid to delete plugin from plugins tab and upload the new version because I have so much content (~1000) that loss of it would be catastrophic 

Thank you so much! 

Anton, Developer