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but cellphones may get half of the message only, as it is limited to 140 chars.

No, the message is still limited to 140 chars, for cellphones or browsers, the link handling is done behind doors.

So where does the phone get the URL, another message?

Phones don't get the url, just the LINK placeholder, you can not navigate on a cellphone.

Now, smartphones, they use browsers, browsers can read html, then they get the url under the LINK placeholder.