Me and my partner want to engage in a sequence of Bitcoin transactions. The first transaction involves me sending $400 in BTC, and the second transaction involves my partner sending me $900 in BTC.
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That offer in itself sounds too good to be true, so you have to ask yourself, what's the catch? Are there any other actions or requirements between these transactions? Or do you really expect someone to send you $900 in return for your $400?
As others have already suggested, your best option is to use trusted escrow.