"claimed through" is correct and can be used in written English.
It is mainly used to describe a process of asserting something or making a request. For example: "She claimed through the court that she had not received the money from the defendant."
But he claimed through gritted teeth that it was now "100% committed".
The excellence of a given learner is usually claimed through a performance comparison with other learners over a collection of data sets.
On an average night, the restaurant serves 250, and the few openings not claimed through the partners go to civilians.
By the end of the campaign he had spent 14 million, but claimed, through a soaring stock market, that his holdings were up to 60 million.
In some areas descent and land rights can be claimed through either parent, so people can belong to both their parents' clans.
Mr. Mulligan has claimed through a lawyer that he was illegally detained in a motel room by police officers who were trying to steal his money.
The agreement allowed a portion of Jewish emigrants' possessions, which they were forced to hand over before they left Germany, to be re-claimed through transfers to Palestine as German export goods.
You won't be able to claim through your travel insurance.
Once they said they weren't responsible for the money and that I had to claim through Austrian Airlines.
After agreeing to an interview, FirstPlus Chief Executive Daniel Phillips canceled, claiming through a harried secretary that he was "very busy".
Creatives on the coasts will claim through omission that nothing culturally significant happens in the Mountain Time Zone.
