To change the #$Microtheory (Mt) that the displayed assertion is asserted in, enter the new microtheory into the input window, then press the [Change Mt] button. The assertion itself is displayed in its EL form at the bottom of the page.
This will delete the assertion from the old microtheory and reassert it into the new one. To simply add the assertion to the new microtheory, while still leaving it in the old Mt, go back to the Assertion Display Frame, click on "Assert Similar", and enter the original assertion using a new Mt. For help with the Assert Similar Formula tool, see The Syntax of CycL.