"genuinely convinced" is a correct and usable phrase in written English.
It can be used to describe someone who truly believes in something without any doubt or hesitation. Example: After hearing her passionate argument, I was genuinely convinced that she was right and decided to support her cause.
I was genuinely convinced that a same-sex marriage law would be largely adopted.
Al-Jazeera has a conspiracy theory that it cannot prove, but of which it is genuinely convinced.
They are genuinely convinced that it's possible to buy positive coverage in the Wall Street Journal, or other international publications.
There is the added risk of governments equating political danger to themselves and their policies (some of which they may be genuinely convinced will save lives) with actual danger to the country.
Senior U.S. officials seemed genuinely convinced that our invading troops would be hailed as heroes, while ordinary Iraqis often talked about fighting U.S. troops with guns, grenades and suicide bombs.
Either because they are genuinely convinced that a particular neighborhood provides an ideal microcosm through which to view society as a whole, or simply because it is the subject they know best, these filmmakers have intensely narrowed the focus of their work.
Brilleaux was a genuinely convincing R&B singer, his nicotine growl tapping into something fundamental about what he described as "music about bad luck".
Novelists might not be able to create perceivable sound, but they're uniquely skilled at creating that context, and if the story is strong enough — the cultural cues ring true, the description genuinely convincing — perhaps the actual thing can fade in significance to the point where it almost isn't even necessary.
Another advantage of this position is that it allows us to admit what has seemed obvious all along: that Al Qaeda members and Palestinian suicide bombers are genuinely, sincerely, convinced that they are doing the right thing.
"A surprising number of activists inside and around Labor parties and progressive politics genuinely seem convinced that the way forward for our parties is to go back seventeen years, to recapture the "new day" which dawned in London in 1997; or even more implausibly, to go back thirty one years, to restore the so-called "reform era" which began in Canberra in 1983," he said.
Alan Pardew seems genuinely delusional, having convinced himself his side do not concede from set-pieces even though the stats suggest otherwise.
