Solution:
There is an excellent tool that certainly eases WordPress migration WordPress (and others) Search and Replace Tool. With that tool it’s easy to search through the entire database for all occurrences of old domain, and replace that with the name of new domain. After replacement all the pictures and widgets should work properly.
The way I’m moving WordPress:
- export and import the database with phpMyAdmin
- transfer the files with FTP program like FileZilla
- edit the wp-config.php settings for a new domain
- search and replace on the database with InterconnectIT Search and Replace Tool