Microsoft has reportedly hinted at Alexa integration for Cortana recently by demoing the two working together to allow the user to interact with one by first activating the other. Microsoft showcased what it would look like if the two smart digital assistants worked together at its Build show back on Monday, May 7, and during the event it proceeded to open up Alexa by asking Cortana on a Windows laptop to open Alexa. This prompted Alexa to activate and then the user was able to initiate an action with Alexa just like if the interaction started with Alexa in the first place.
The same thing was done for the reverse, asking Alexa to open Cortana, which then prompted Cortana to activate on the Windows machine for use. Currently this isn't a feature which is possible for end users to access but it does display that it's seemingly possible to make the two assistants play off of each other if anyone should feel the need that such a thing would be useful. What's more is that this is reportedly not the first time that Microsoft has hinted at such a capability, so this might suggest that the company is working on making this an available function on certain devices pretty soon.
It does appear that the integration is coming at some point as Microsoft has a signup page available for users that will tell you when the integration is available, but it's also noted that it is in a pretty early beta phase with very limited capabilities, so it could also be a while before anything is announced officially for use by the public. That said it's an interesting feature that users will get to have access to at some point if they happen to use those two assistants, so it might be worth keeping an eye out for if you're a Windows user with an Echo speaker.