Hail to yee all,
For information, in case anybody would come across the same problem I had and would not be more expert as I am. (Highly UNprobable, but nevertheless...)
If you installed the LTS kernel and your bootloader is Grub (which is highly likely), just run update-grub and it will take care of everything.
If, for some reason, the bootloader of your box is NOT grub, then, it will be Syslinux. And syslinux won't automate the display of your new kernel at splash. You will have to edit manually the configfile of syslinux. To help you, there is 1.
this page of documentation.
Now if, like I have, you mess this config file and are stuck at splash, you may want to have a look at 2.
this thread too.
Now, back to other stuff. I can now confirm that, with this kernel, the package
exfat-utils alone is enough to take good care of mounting exFAT partitions.
And, YEEES, kernel 4.19 will get your system more responsive!!! I'm so glad I installed it!
Cheers