Like any other ASx file transfer, AS1 file transfers typically require both sides of the exchange to trade SSL certificates and specific "trading partner" names before any transfers can take place. AS1 trading partner names must really be email addresses. (AS1 is the only ASx protocol that contains this requirement.)
Variations
Direct connections to each mail server - AS1 clients can usually be configured to connect directly to your partner's email server rather than your local email server. Doing so avoids multiple "relay hops" but usually involves some additional firewall configuration.
Shared mail server - Your organization and your partner could agree to use different email accounts on the same physical email server, hosted at your data center, your partner's data center, or any other email server in the world. Doing so avoids multiple "relay hops" but usually involves some additional firewall configuration.