Mohammed Aqib Imran, 22, made arrangements to travel for jihad, around the time Naa'imur Zakariyah Rahman, 21, was set on a suicide attack on the heart of Government.
Rahman, from Finchley, north London, helped his like-minded friend by recording an IS sponsorship video for him, the Old Bailey heard.
The pair were snared by a network of online role-players from the Met Police, MI5 and the FBI.
Rahman's plans to kill Theresa May were scuppered when undercover officers handed him a jacket and rucksack packed with fake explosives.
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Following a trial in July, Rahman was convicted of preparing acts of terrorism and Imran was found guilty of possessing a terrorist handbook.
Rahman also pleaded guilty during his trial to assisting Imran in the preparation of terrorist acts by recording a sponsorship video.
Following a retrial, former student Imran was further found guilty of preparing acts of terrorism abroad on or before November 28 2017.
Prosecutor Mark Heywood QC told jurors: "At the heart of this case is a developing radicalisation in the minds of two men who came to know each other online and afterwards met and began to collaborate.
"Both thought about travelling abroad to further their cause, going to a conflict zone such as Syria to lend support to violence. Each also contemplated carrying out terrorist acts of violence here in the UK.
"Mohammed Imran - he elected to travel and set about assembling money, acquiring a fake passport, engaging in research and otherwise equipping himself with the information and means to travel aboard for violence for terrorist purposes
"In the case of the other, Naa'imur Rahman, his conclusion was that lethal violence here, directed at the very heart of the UK Government, was the only effective way to pursue his intentions.
"Before his arrest prevented it, he was, he believed, just days away from his objective, which was no less than a suicide attack by blade and explosion, on Downing Street and, if he could, upon Prime Minister Theresa May herself."
The court heard how Imran's preferred destination was Libya or possibly Jordan with a view to onward travel to Syria.
He had saved money to pay for a fake passport and researched travel options, the court heard.
He downloaded the manual How to Survive in the West - a Mujahid's Guide 2015 with a view to joining IS, the jury was told.
Imran, from Sparkhill in Birmingham, denied the charge against him, claiming he only wanted to get married to a woman in Denmark he had met online.
The jury deliberated for just under 18 hours to reject his explanation and find him guilty of preparing to engage in acts of terrorism.
In August, Rahman, who is originally from Birmingham, was jailed for life with a minimum term of 30 years.
Judge Nicholas Hilliard QC, the recorder of London, requested a report from the probation service before sentencing on any potential "future risk" from Imran, as it was "a really important question, the safety of the public".
Imran is due to be sentenced on January 25.
Following the verdict, Jenny Hopkins, head of the Special Crime and Counter Terrorism Division in the CPS, said: "Mohammad Imran was desperate to join Daesh rather than remain in the UK.
"He was ready to give up everything to kill in the name of a warped world view."