If the contradictory information stacks up, it could mean that Sroubek may have committed an offence under the Immigration Act - which could trigger liability for deportation or criminal charges.
Following a particularly awkward Question Time on Thursday in which the minister repeatedly avoided answering questions, National MPs took to Twitter to use the minister's former words against him.
"I want more facts!!! That's what it's all about. Why the wall of silence from Govt?"
Lees-Galloway said in January 2017.
He added in another tweet: "That's the problem with the use of Ministerial discretion - it's not transparent..."
Senior MP and Twitter provocateur Judith Collins retweeted both of these, adding in one: "I agree..."
National MP Mark Mitchell joined in the retweeting action, saying: "Please support Iain Lees-Galloway's plea to Iain Lees-Galloway for more facts and to drop the wall of silence from Gov."
National MPs Chris Bishop and Simeon Brown also added their two cents.
Lees-Galloway had been asking about the granting of citizenship to tech billionaire Peter Thiel.
In Question Time on Thursday, Lees-Galloway repeatedly ducked questions from National's immigration spokesman Michael Woodhouse.
"It is not in the public interest for me to divulge the information that I did or did not have in making that decision," he said in response to questions about whether Sroubek might be in danger if he were deported.
His lack of answers earned howls of interjection from the Opposition and warnings from Speaker Trevor Mallard.
"Clearly, the public interest test is one which should be a high test when it is applied, because otherwise it can be used to avoid proper scrutiny of ministerial decision-making," Mallard said.
"I do want to make it clear to Ministers that the fact that they are not required to generally disclose something under a statute is not a protection for answers in this House."
The investigation is expected to take up to three weeks.
