Hey, I'm replying to a previous post, not to your most recent one, so that you are able to edit that last one: you do NOT want your email address and other info out here in the open forever!!!
Go and delete at least the images, please. If you don't have an Edit button at the bottom of that message, then probably because you're on you iPhone or so, but not in Safari on your Mac...
Tip for the future: before posting, use an image editor to make personal data unreadable...
Other than that, don't worry, it's fun! :D
The reason why the iPhone can't send via Tagra is simple: the Tagra SMTP server does not let mails through that are sent from an email address with a different domain than their own. You are using a @hotmail.com address with the tagra.com.mx SMTP server, and the server blocks this. You can only use a @tagra.com.mx email address to send with that server.
In the account, please replace your "Email" address ending in @hotmail.com with one ending in @tagra.com.mx. Then you will be able to send from your Tagra account.
FYI, more and more ISPs block this mail relaying that you were trying. The reason is simple, they want to make it harder for spammers to abuse their servers and use a fake identity, or one that is harder to be traced. Otherwise an ISP risks that his SMTP server is getting blacklisted, meaning most incoming mail servers will refuse mails coming from them.
Accordingly, and this is true for any mail client, iPhone as well as Mac, if you want to send mail from your Hotmail address, you must setup a new, separate account on your device which uses Hotmail servers.
In Apple Mail on your Mac, I am certain that the reason for you being unable to send from the Prodigy account is that you have no authentication specified ("...login not required"). The SMTP server will surely require your account credentials. Otherwise anyone could send mails through that server...
So, in the Prodigy account preferences, under Account Information, click on the Outgoing Mail Server (SMTP)... yes, the name in the drop down list there. As the list opens, click on Edit SMTP Server List. In the window that opens, select the Advanced tab. For Authentication, choose Password, and enter your username and password below. OK, and one more Save (I believe) when closing the Preferences, and you should be good to go.
That's it, unless I overlooked something.