Looking on the internet deeply has found these results:

that have became is the most popular phrase on the web.

that became 117,100,000 results on the web	that have became 189,800,000 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
Henry Wadsworth Longfellow in 1860 wrote a poem that became famous here. Filumena was the play that became the movie, Marriage Italian Style, with Marcello Mastroianni and Sophia Loren. Dow Chemical had just bought Union Carbide, a company that became infamous in the 1980s. A chip that became the basis for what's in every cell phone today. The house that became a sinkhole. The you that became The Flash. And then they just started calling me Sugar and that became my nickname. A passion that became a profession?	After Mal became pregnant, that became our home. You said Vázquez became your lover since you became widowed. My situation became clearer because everything else became unclear. We have evidence that Morgan became ill that night. The minute things became complicated, you became dispensable. We have evidence that Morgan became ill that night. The very words that they have sung Became their last communion You should have said that you became a dance doctor!

that became

117,100,000 results on the web

that have became

189,800,000 results on the web

More popular!

Henry Wadsworth Longfellow in 1860 wrote a poem that became famous here.
Filumena was the play that became the movie, Marriage Italian Style, with Marcello Mastroianni and Sophia Loren.
Dow Chemical had just bought Union Carbide, a company that became infamous in the 1980s.
A chip that became the basis for what's in every cell phone today.
The house that became a sinkhole.
The you that became The Flash.
And then they just started calling me Sugar and that became my nickname.
A passion that became a profession?