On Friday Lees-Galloway said evidence that Sroubek had returned would have been "very useful" and would have "likely" led to a decision to deport Sroubek.
Instead Lees-Galloway granted Sroubek residency, even though Sroubek was in jail for drug-smuggling.
After learning that Sroubek may have been back to the Czech Republic and that his estranged wife - who had supported Sroubek's case - may in fact be fearful of Sroubek, Lees-Galloway ordered a review of the case.
He eventually issued a new deportation notice to Sroubek, which Sroubek is appealing.
Woodhouse said the idea that the Minister may have made a different decision was "absolutely ludicrous".
"If this decision rested on Sroubek's claim of fear of persecution, and that would have been undermined had he have gone back to the Czech Republic, the Minister should have asked the obvious question.
"He did know that he had flown to Frankfurt at least once. The Frankfurt travel should have set off alarm bells and prompted the Minister to ask questions of officials.
"They could have easily gone back to Sroubek. He's in prison. He'd have folded like a red hot Mars bar if they'd gone back to further interview him."
Immigration officials could have also asked Sroubek, but "they probably didn't think they had to because they had such a compelling case".
But Lees-Galloway said he asked officials.
"I asked if it was possible to ascertain whether he had returned or not, and was told it wasn't.
"Mr Woodhouse [a former Immigration Minister] well knows that it's only appropriate for Ministers to consider the information presented to them."
Immigration NZ general manager Stephen Dunstan said on Friday that the information in the 2012 email was unverified and "does not show up in the official travel movement history for Mr Sroubek".
National has also been trying to find out who supported Sroubek, but many of the names in the documents released on Friday were redacted.
Woodhouse said he would likely appeal to the Office of the Ombudsman for that information to be released, saying public interest outweighed privacy concerns.
He has repeatedly asked whether Richie Hardcore, a friend of Sroubek's who texted the Prime Minister after news broke about Sroubek being granted residency, had supported Sroubek's immigration case.
Lees-Galloway has said during Question Time that Hardcore had not communicated with him prior to his decision, but Woodhouse pointed out that didn't mean Hardcore couldn't have made a written submission supporting Sroubek.
The documents also show that Immigration NZ started building a case to deport Sroubek in 2012 after he admitted to using a false identity to gain a resident visa.
Even though Sroubek was discharged without conviction, he was still liable for deportation.
Immigration staff repeatedly appeared frustrated that Sroubek - also known as Jan Antolik - avoided deportation.
Immigration Technical Specialist Janene Smith emailed a colleague following a Herald story in 2017 about Sroubek's appeal against his conviction for drug-smuggling.
"We prosecuted him for using a false identity but Mr Antolik seems to have the luck of the charmed - the Judge discharged him without conviction so that he wouldn't be deported," Smith wrote.
Following another Herald story about Sroubek being discharged without conviction, Smith emailed colleagues saying: "S'pose you know this John? GRRR!!!!!"
Immigration resolutions team analyst Angela Vinsen replied: "He has been on our radar for a while now."
Smith also wrote to Interpol in Wellington in February this year, saying deportation would be preferable to extradition because it would strip Sroubek of the right to return to New Zealand in the future.
