A map for the future mission

@Number1Jeww

Try adding swtor.exe and launcher.exe to your anti-virus / firewall safe / exceptions list in case they are blocking or deleting files.  Next I would go ahead and run a repair:

Non-Streaming launcher - Log into the launcher but don't click Play. Check for small letters "ST" in the bottom left corner. If this is NOT present, With the new launcher after login , select the username pull down on the top right and select settings, then press repair.

Streaming launcher - If the letters "ST" is present, close the launcher, right mouse click on the game shortcut, select open file location and delete the BitRaider folder. Then start the launcher.

Afterwards try the mission again, also if your able to go to the Map and on the bottom right above the mini map if you see a drop down use it to change your instance and try again.  You can also try press spacebar rapidly to skip past the conversation.

Also try lowering your graphics settings to see if it will force the conversation through.

Lastly if the above doesn't work and your using the Streaming launcher you can try to switch to the non-streaming launcher and see if that gets around it.  I would only do this as a last resort as this is a complete download of the game again

right mouse click on game shortcut and select open file location

open the launcher.settings file in notepad and locate the below line and edit to the below

, "PatchingMode": "{ \"swtor\": \"SSN\" }"
, "bitraider_disable": true

SAVE the changes.
Delete the BitRaider, Movie and Asset folders then start the launcher.