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Dunno if I have enough info to yet make a suggestion, so I'm going to ask a few questions. First, what model handset are you using? Second, which app/email client?
In gmail. From inbox, tap once on message (that opens it for viewing) . Long press on subject until the edit drag handles appear. Drag the handles to highlight the whole subject. Press copy icon (upper right hand corner).
That's it. That's not lightning fast, but I think it's the fastest way to do it from gmail (not sure about other mail programs).
The alternative in gmail is to "respond inline" and use normal editing tools to select...that takes an extra step or two and it's a little harder to select when the subject is mixed in with the rest of the message