Correct?

English as a Second Language English Vocabulary, Grammar and Idioms
1
  1. She justified her claim with her specious argument.
  2. Her specious claim made us suspicious of her intention.
    Are these sentences meaningful and logical?
    If warranted, please rephrase them.
    thanks.
2

Do you mean to say both her argument and her claim are ‘specious’? If not, the sentences can be recast thus:
She tried to justify her specious claim with her argument, which made us suspicious of her intention.