"wrongly believe" is a perfectly correct and usable phrase in written English.
You can use it to express that someone has an opinion that is inaccurate or false. For example, "She wrongly believed that the meeting had been canceled."
Josephine Bersee, Hong Kong Build better buildings Many people wrongly believe that earthquakes kill people.
Buzz! Boomer, you and the Clintons wrongly believe Miller Lite tastes great.
Community and religious leaders wrongly believe that sexuality education promotes promiscuity.
Many people wrongly believe that China can improve its foreign relations only by significantly increasing economic aid.
Most supplier sales reps wrongly believe that satisfying customers' every request for information and support makes buying easier.
Some managers wrongly believe that tangible resources are always more meaningful to employees than being treated decently.
Many, he noted, wrongly believe that the problem is "the other guy" and that they don't make mistakes.
And because Britain deploys conventionally armed Tomahawks, a target country detecting a missile launch might wrongly believe it was under nuclear attack and react accordingly.
One finding that may grab the attention of policy makers is that most Americans wrongly believe that anything having to do with religion is prohibited in public schools.
The new minimum retirement age is unpopular among youngsters who wrongly believe that jettisoning older workers will open up job opportunities for them.
Many Americans wrongly believe that while they are dutifully paying taxes, a lot of other people — especially lower-income people and immigrants — are not taxpayers.
