Assets cannot be moved properly using the JCR Session.move API. Instead you must use the PageManager.move API.
PageManager pageManager = ((PageManager)resourceResolver.adaptTo(PageManager.class)); Resource sourceResource = resourceResolver.getResource("/content/dam/example.jpg"); String destinationPath = "/content/dam/test/example.jpg"; pageManager.move(sourceResource, destinationPath, null, false, true, null, null);
Unfortunately, that method call doesn't fully include everything that is done by the com.day.cq.wcm.core.impl.commands. AbstractCopyMoveCommand class which handles the request from the UI. To fully simulate the UI, you would have to internally fire off this request using the SlingRequestProcessor.
See this article for details on how to internally fire off such a request:
The request would be:
cmd=movePage integrity=true _charset=utf-8 destParentPath=/content/dam destName=test1.png srcPath=/content/dam/test.png