Take a look at this option: https://github.com/parse-community/parse-server#custom-pages

You can create your custom pages and pass customPages option to Parse Server with their locations.

You can find the default ones and use them as template in here: https://github.com/parse-community/parse-server/tree/master/public_html

Parse Server 5.0 will contain the PagesRouter which should make translation of pages easier. It is currently only available on the master branch, if you want to give it a try.

See https://github.com/parse-community/parse-server/pull/7128

As Davi Macedo showed, I create the files and solved the problem with them. But I don't know if Parse should automatically replace the files in public_html. In my case just put the files there was not enough. My solution was create /public/pages with the custom files, and point my customFiles config like that:

customPages: {
    passwordResetSuccess: base + "/public/pages/password_reset_success.html",
    verifyEmailSuccess: base + "/public/pages/verify_email_success.html",
    invalidVerificationLink:  base + "/public/pages/invalid_verification_link.html",
    invalidLink:  base + "/public/pages/invalid_link.html",
    choosePassword: base + "/public/pages/choose_password.html",
    linkSendSuccess: base + "/public/pages/link_send_success.html",
    linkSendFail: base + "/public/pages/link_send_fail.html",
  }

Besides, to choose password page I used this file: https://github.com/parsegroundapps/pg-app-tynwrjdecdmr69ke5d8fec6ixljzx5/tree/master/public/pages

Another detail is that the file choose_password.html on the repository above makes de POST request adding "/1/" to url, but in my case, I needed make the url pointing to "/parse", so I replaced the line 181 to

var base = window.location.origin + '/parse/';