Yes this is U126.
To look at one manuscript, Vaticanus Palatinus Graecus 182 (Page: 176r), we have αὐτῇ
By changing αὐτῇ to αὐτήν, a little more sting is given to this tame remark: "he thinks that she preaches."
I do like the option of αὐτὴν, and αὐτὴν serving as the accusative subject of παραινεῖν -- "νομίζειν αὐτὴν παραινεῖν" and this could be interpreted without a sting: "he considers her [capable of] advising"