Earlier quoted context omitted.
No, while entanglement acts instantaneously across a large distance, there's no way for that "signal" to carry any information. In order to complete the teleportation the two parties must somehow communicate in order to convey an additional piece of information. This communication would be classical and slower than light.
Any chance that communication could happen _before_ the measurement? Entangle some matter, give half of it to the space team and then have inter-stellar walkie talkies?
Imagine that you have 2 coins and give one to someone on earth to flip and one to someone on the moon to flip. The outcomes in either location is random 50/50, but interestingly they are perfectly correlated (HH, TT). When you flip a coin you don't have the ability to pick it's outcome. The only thing you can pick is whether or not to flip it at all. So, imagine you want to communicate one bit of information from earth to the moon and decide that a 1 will be encoded as "flip the coin" and 0 as "don't flip the coin". When you're standing on the moon and want to reveal the information you flip the coin and see e.g. H. There are two ways this could have happened: either the earth coin had already been flipped and showed H or the earth coin had not yet been flipped and you just randomly got a H. In other words, the outcome by the flip is useless by itself.