So, here is how I solved. (I set up all the stuff some weeks ago, so please forgive if my explanation is not so accurate).
1. Transfer your first wp site onto your new server with the standard wp-migration procedure.
2. Create a new, blank, WP blog on your server using the installer provided by your hosting service. The new blog will be placed in a new directory and will share the only database you have.
3. Now access your myphp admin page on your new server and check your database tables. You will see that they have two different prefixes – probably wp_ and wp0_. The first is the prefix of your first blog (the one you have moved with wp-migration), the second prefix refers to the tables of the new, blank, blog that you have just created. Take note of this prefix.
4. Now go back to the SECOND website you wish to transfer – the one that is still on the old server waiting to be transferred. Change its the table prefix in order to make it exactly the same as the prefix you just took note of (probably wp0_). Fortunately there is a WordPress plugin out there that will do the job for you – just look for it. Changing the table prefix should not affect your old blog.
5. After this, check your database to see if the table prefix have changed. If so, use the Export function to export the tables into a file, and save it somewhere on your pc.
6. Now return to the new server, go to the php database admin and import the new tables file. This will overwrite the tables of your new, blank blog, leaving the first blog’s tables unchanged.
7. Now use your Ftp client to manually transfer your wp-content folder from your old, second website to your new server, so that the wp-content folder in is replaced in the directory that hosts the new, blank blog. Make sure you do not accidentally overwrite the first blog directory instead!
8. In order to make the 2nd blog work on the new server you will probably have to adjust username, password and domain records in the database, so that they match your wordpress information.
