I've done several BTC to Monero exchanges using Shapeshift.io and my Monero Wallet on my Android Phone. I use the Freewallet.org Monero Wallet from the Android Store. I also have a Ledger Wallet which holds my Bitcoins, but you can use any Bitcoin Wallet Receive Address with Shapeshift.io. There are several videos on Youtube that show the mechanics of the Shapeshift.io interface.

The non-intuitive part of the Shapeshift.io transaction process is that you will send Bitcoin dollars to a Shapeshift.io Bitcoin address and they will then send those same funds minus a transaction fee to your Monero Public Address.

I would start with a small amount to understand the process and then send the larger amount on a second or third transaction, noting that each transaction will produce a small fee for Shapeshift.io.

wowww 40btc? how did you do that?

Of the exchanges Poloniex has the liquidity. I haven't been on there since they instituted kyc polices. There are different levels with different requirements and different withdrawal limits. Sorry I don't have specifics. The exchange with the second best liquidity is bittrex with significantly less volume but 40 btc should be able to be done with some patience.

The other alternative is ShapeShift. No account needed. Just send them btc and they send you Monero. You can't send 40btc at once and will have to make several transactions. The price is approximately the sell side on the exchanges + 1%. You will need a Monero wallet for them to send to.

I assume you would not be keeping your coins on an exchange so you would have to set up a wallet anyway. I would not recommend the web wallet for that amount. You would need to install the client, download the blockchain and set up a wallet or wallets. It is not difficult to do. Currently there is a CLI wallet but a beta GUI wallet is being released this week. This still requires you to install the client and download the blockchain before using the wallet.

If you need help or adviceay it may be best gotten on IRC. Channel #monero https://webchat.freenode.net/ select a name and the channel #monero click the I'm not a robot box do the captcha and hit connect

If you'd like i can assist in the exchange. PM me for details.