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Yes, it's OK. But 'I have understood' is a little uncommon (note to others: does anyone know if there is some restriction on the use of stative verbs in the perfective aspect? Both 'I have...

Well the problem with the original dialogue is just that the second speaker should use the past simple, not the present perfect.

For example:
Have you been to London?
Yes, I have.
Did you like...