Fe_login doesn't send email from forgot password template

Question

I have a TYPO3 site, based on 9.5.31 and I'm trying to setup fe_login for this. I can login as FE user, but Forgot a password doesn't work - nothing is sending by email. All other email is working properly, test email from InstallTool - too. This is part of template what I using:

<!--###TEMPLATE_FORGOT###-->

###STATUS_HEADER###
###STATUS_MESSAGE###


<!-- ###FORGOT_FORM### -->
<form action="###ACTION_URI###" method="post">
    <div class="felogin-hidden">
        <input type="hidden" name="tx_felogin_pi1[forgot_hash]" value="###FORGOTHASH###" />
    </div>
    <fieldset>
    <legend>###LEGEND###</legend>
    <div>
        <label for="tx_felogin_pi1-forgot-email">###DATA_LABEL###</label>
        <input type="text" name="###FORGOT_EMAIL###" id="tx_felogin_pi1-forgot-email" />
    </div>
    <div>
        <input class="felogin_submit" type="submit" name="submit" value="###SEND_PASSWORD###" />
     </div>
    </fieldset>
</form>
<!-- ###FORGOT_FORM### -->
<p>###BACKLINK_LOGIN###&nbsp;</p>
<!--###TEMPLATE_FORGOT###-->

I'm tried to set exposeNonexistentUserInForgotPasswordDialog to check something about email is exist, but with no result.

Any ideas?

NB - I'm using fe_manager for FE user register