The second sentence probably isn't right. It would help to know what you are describing. What is being done, and what is "it"?
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LiveinjapanDo that when it recovers.
Does the sentence below have the same meaning?
Do that on the recovery. It depends on context, as MrWordy suggests.
If "the recovery" is idiomatic in this particular endeavor, then they'd mean the same thing. If you're talking about surgery or the economy, I'd say "yes."
(when he