The phrase "act even though he" is correct and usable in written English.
It can be used to describe a situation where someone takes action despite a particular condition or circumstance involving "he."
Example: "She decided to act even though he had expressed his disapproval of her plans."
Alternatives: "proceed despite his" or "take action regardless of his".
Because the novel was a commodified art form (like it or lump it) various avenues of "cultural performance" were made possible; when Iain Banks's calling for a cultural boycott of Israel in 2010 was a powerful act, even though "he writes about space ships" and not Palestine.
Lyndon Johnson passed the Civil Rights Act even though he knew it would cost the Democrats the South.
I would later learn that my father was staggered by Morrison's act, even though he regarded it as profoundly misguided.
The reason cited by the board is that Lance Corporal Schumann "didn't die by a hostile act," even though he was deployed in a war zone.
He apparently didn't act, even though he was the leader — the so-called leader — of a charity devoted to helping vulnerable children.
And he accepted extra Medicaid dollars from the federal government distributed under the Affordable Care Act, even though he has since boasted he would "repeal Obamacare" if he reaches the White House.
Dick Fuld's wife had the poor judgment of shopping in Hermes and the reporters caught her in the act, even though she spurned a tell-tale orange bag.
"A lot of the Democrats hated the Patriot Act even though they voted for it, and they certainly didn't want to see it made permanent.
The geese are protected by the Migratory Bird Treaty Act, even though they are not an endangered species and no longer migrate, said Bobby Horvath, a licensed wildlife rehabilitator in Massapequa.
A few activist groups have threatened to file suit against the bus program under the California Environmental Quality Act, even though they take cars off the road.
I believe secrets about human behavior, which provide insights into the way people act even though they can't tell you why, are levers for creating user habits and competitive advantage.
