You are correct: "thru" means "through". "Thru" isn't actually a word; it is simply "shorthand" for the word "through". The word "thru" became popular when US fast-food restaurants started adding drive-through lanes for cars to order and pick up food orders. Since "through" took up so much space on signs, they simply created the word "thru" to save space. In your example, the phrase "follow thru" (or, follow through) means that she will take the necessary steps to investigate the potential job. Let me know if you need further explanation.

Thru is just a short way of writing or texting 'through', like you guessed. Follow-through means the person plans to take the information they've been given, and learn from it, perhaps take action on it, until they reach the end. The end might mean making a decision, or completing a project, and so on. In fact, the process of 'doing' can be called the follow-up, and the end of the process is more of a follow-through. If my answer is confusing, you can FOLLOW-UP with another question. Please do FOLLOW-THROUGH to get the best answer.

Hello echo floating, Thru is a variant of Through. They do mean the same thing. I personally do not use Thru but that is just a choice. As for the meaning of "following thru or through". It means seeing something to its completion. She is saying she will take the info given to her and use it to the best of her ability to get the job. I hope this helps.