If you do not mind using a 'helper' attribute for the selection in the Mendix application, you could do the following:
Doing the above will require a Java action, since if you'd use toString for this you'd get the enumeration value and not the caption. So what you would need to do in the BCo flow is call the Java action (which has the enumeration as argument) and pass the enumeration value of attribute B. The java action will return the caption of the enumeration as String, so you can then just use a Change activity to write this value to attribute A.
As for the Java action, it should have the following code in the user code area:
// BEGIN USER CODE
if (Enumeration == null){
return "";
}
return this.Enumeration.getCaption();
// END USER CODE
Where 'Enumeration' should be whatever name you gave to the enumeration argument of the java action.
You could map the title to a different entity and then select an object of that entity when selecting a title.