I don't see why it doesn't work this way. I've been the option "Put sent messages in: #mh/Boîte aux lettres/sent" for a long time now and I just checked on my gmail account and I can see the mail I send from claws-mail.
To send your email are you using the Gmail SMTP server? (smtp.gmail.com). On my settings, I use SMTP on port 587 and I also have SMTP AUTH and STARTTLS enabled.
You could also check that your "From" field is correct and matches your login to Gmail.
That's all I can think of.
Hope this helps.

thanks for this useful guide on setting up Claws to play nicely with Gmail/GoogleHosted accounts.

I followed it but I'm having just one little issue, I think.

I've chosen to save the sent mail on the local Mailbox (MH), as you suggest, by configuring the "Put sent messages in: (...)/sent" option.
Then, sent mails are saved on that folder

But then, contrary to what your guide says, sent mails are not being saved also on the imap "Sent" folder.
It's weird, because I wonder: how does Gmail "know" that I'm saving my sent emails locally, so they "decide" not to save it also on the imap "Sent" folder?
Maybe Claws mail somehow "flags" the email being sent and so, when Gmail process it, Gmail decides not to save it on the "Sent" folder?

Any advice will be appreciated.
Thanks