The JavaDoc kernel with Dropbox and Android extends what you need to do a little more, showing an alternative AndroidAuthSession constructor:
When the user returns to your application and you have tokens, just create a new session with them:
AndroidAuthSession session = new AndroidAuthSession( myAppKeys, myAccessType, new AccessTokenPair(storedAccessKey, storedAccessSecret));
I assume that you just need to instantiate the DropboxAPI object, and you are good to go without startAuthentication () ... endAuthentication (), etc.
DropboxAPI<AndroidAuthSession> mDBApi = new DropboxAPI<AndroidAuthSession>(session);
I have not tried this, but it is essentially the same as Greg said.
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