Someone who is sentenced to 20 weeks would normally be released on licence after 10 weeks. The terms of licences vary from one offender to another but one of the standard terms, which applies to everyone on licence, is that they may not travel abroad without permission. (Permission would only be granted in exceptional circumstances, e.g. if a near relative was gravely ill in a foreign hospital).
The licence period normally runs to the end of actual court sentence so, if your friend is released after 10 weeks, there will be a further period of 10 weeks during which he may not travel abroad.
After the end of the licence period your friend can travel to any EU country without any problems. Many non-EU countries, however, would refuse to grant a visa to anyone with such a conviction. (e.g. it's extremely likely that the USA or Australia will ever allow your friend to visit their country).
Chris