"she supposes that" is grammatically correct and is commonly used in written English.
Example: She supposes that the movie will be sold out by the time they arrive at the theater.
She supposes that makes her a native New Yorker, whatever that means.
She supposes that he comes up during intermission time.
She supposes that Lourdes knows how to make husbands disappear, and to some extent she's right.
In 'Mozambique Channel' she supposes that she was, instead, on one of the boats that were bombed on the way to South Africa.
She cannot hear through her window, but she supposes that each man is singing to his woman, and each woman to her man.
At the box office, there was the routine question, "D'you have a season ticket?" She supposed that was to have been bought when the Rendall Harris engagement was first announced.
She supposed that that was what he was fed up with.
She supposed that she was suffering from bile, but the symptoms make possible a modern clinical assessment that she was suffering from Addison's disease.
She supposed that he was trying to impress her — and she "tried explaining to him that it would be better if he didn't try to.
She supposed that it was her time of life, though it felt more as if she were holding herself apart from her own body, afraid to leave off being vigilant for a moment.
Since she did not see him walking to the dam, she supposed that he was taken there by military jeep now, and brought home in the same way in the evening.
