None of the solutions mentioned so far worked for me. Remote part just couldn't connect.
According to H2's official documentation:
To access an in-memory database from another process or from another computer, you need to start a TCP server in the same process as the in-memory database was created. The other processes then need to access the database over TCP/IP or TLS, using a database URL such as: jdbc:h2:tcp://localhost/mem:db1.
I marked the crucial part of the text in bold.
And I found a working solution at this guy's blog:
The first process is going to create the DB, with the following URL:
jdbc:h2:mem:db1
and it’s going to need to start a tcp Server:
org.h2.tools.Server server = org.h2.tools.Server.createTcpServer().start();
The other processes can then access your DB by using the following URL:
"jdbc:h2:tcp://localhost/mem:db1"
And that is it! Worked like a charm!