Lateral offer - should I take it?

First on the story, second on the process:

On the story, the most important thing is to have a solid story that makes sense without mentioning exits. If you want to go work for a HF, PE shop, or AM that's great but be sure to never mention you want to gain these skills for a job down the road. May be common sense but not always common practice. In terms of positioning, I would ask yourself what kind of skills, impact, and overall contribution do you get in this position? This is a useful framework to answer the question. Let's break down what this could look like:

• Skills: "As someone who has invested from an early age, I've always been fascinated by understanding the operations, drivers, and future outlook of a large company and crafting a story around it. Being able to work at XYZ EB gives an incredible platform to work on companies that interact with consumers and drive the economy on a daily basis and I find this skill set incredibly satisfying and attractive"
• Impact: Something general like being able to drive multi-billion dollar deals that shape XYZ industry and drive the future of innovation, value creation, etc is a pretty solid and general answer here. If you're in tech mentioning "I am wanting to come to XYZ EB since the deals that XYZ EB is able to drive and act as a strategic advisor for truly transform the industry and the tech we interact with on a daily basis. For instance when XYZ EB advised ABC on acquiring DEF I found this incredibly interesting since it allowed ABC to cross-sell additional products to their customers, drive additional value, and synergistically grow the company"
• Contribution: big one here that many overlook. Mention something about the size of the deal team and how that is good. If it's an EB, mentioning that you "are given a large amounts of responsibility to become more competent and confident is something that is very important to you" mention some more material about how you work on taking responsibility in other jobs / in uni and you have a solid case here.

For me to network, we all have downtime in the middle of the day at times when a project is slowing down. You can easily find 30 minutes to take a call during the day and duck out during your lunch to go take it out of the office. Most of my networking messages, emails, and calls I did at night with bankers, for interviews you can typically go as late as 7:00 pm local time no problem, and if needed during the day duck out.

Make sure no matter what, tell no one you're doing this. Even your closest coworkers, the upside to telling others is nill. Once you leave your coworkers in banking will not really be your close friends and if one person goes and tells your VP / staffer (saw this happen to another analyst) then the downside is significantly worse than the upside,  I would not worry about people at other banks reaching out to your firm. So long as you're not sharing LinkedIn posts from the bank, following the other bank, etc then you should be good. If you really get into the networking process consider using the LinkedIn premium free trial as you are easily going to max out your searches if you're doing a cold networking process.