"jump back into" VS "jump back in" aka does it even exist?

Dear all,

I'm in the middle of writing an email to one of my students who missed so my classes. I'd love to use the following sentence:

• "We have just started unit n. 12, which may be a great opportunity for you to jump back in."
  • Is the phrase correct? I tried to google it but had no success. Does the phrasal verb even exist?
• Or should it be "We have just started unit n. 12, which may be a great opportunity for you to jump back into"?

And while we are at it, which one of these phrases is correct as well, and why? In other words, which one of them would you use in the very same email?

• "Peter and Maria are missing you, and so am I!"
• "Peter and Maria miss you, and so do I!"

Thank you so much! May you have a good one!

T.