Finally I've got things sorted.
The problem with Securitycheck Pro installation described in my initial post is caused by wrong DB collation. My datababase collation was set to "utf8mb4_unicode_ci". After changing it to "utf8_unicode_ci" the problem was over and it was possible to install plug-in properly.
More detailed information about the problem and a couple of possible solutions you can find under this link:
And if you are not very familiar with phpMyAdmin here is the simple step by step explanation how to change the database collation:
That's just for the record!
Thanks Jose again for your assistance!!