Can I detect 0.8 volt with a relay or something?
Here is the chip datasheet , it's for a different package but the same. 

I see that the LED output is sending a pulse at the end of the message. Usually this is used for loop playing but we can use to reset a flip flop at the end of the message. The start can is given by the play button that , inverted, can set the flip flop.  







simulate this circuit &ndash; Schematic created using CircuitLab

CD4044 can be used, the E (enable ) input tied to VCC.