J2EE is defined in terms of WARs, not "folders". A J2EE webapp is according to the spec, a WAR or EAR (except Tomcat doesn't handle EARs), which is a JAR (ZIP) archive with a particular structure plus certain controlling "files" within that structure.
Tomcat is one of many webapp servers that supports the notion of an "exploded" WAR, which is simply WAR which has been unZIPped. So the easiest/safest way to transport a webapp to another Tomcat is like this:
1. "cd" to the TOMCAT_HOME/webapps directory. Or wherever the webapps have been deployed, but I'm assuming the default.
2. If there is both a "xxxx" and an "xxxx.war" file in that directory, delete "xxxx.war". Tomcat always uses the exploded WAR if it sees both plain and exploded webapps in its directory, so the existing war isn't what's actually being used.
3. create a (new) WAR from the exploded WAR, like so:
This should JAR (ZIP) up the WAR into a warfile.
4. Transfer the WAR file to the new Tomcat's webapps directory.
5. If you had an external deployment descriptor for the webapp (generally a Context in the TOMCAT_HOME/conf/Catalina/localhost directory), also copy that to the new Tomcat's conf/Catalina/localhost. Change any options which need changing. For example, you might want the copy to talk to a different database.
That's all there is. At least unless your webapp was so crude as to have written data files into the WAR. Which it shouldn't.
An IDE is no substitute for an Intelligent Developer.