Direct answer to your question first:
How can I ask my boss to relax this requirement?
Option A: You can mention to your boss casually that it's giving you some hard time doing so since English is not your first language, but the excuse only work for a period. If you want to keep the position (and it's pay-level), you got to prove yourself fit it.
Option B: Or, if you have decided on this, you can ask to return to your previous position, which may leave a bitter taste if it is your boss who intend to promote you. And It may leave a unmotivated image to your boss and your HR, which may or may not affect your future career inside this company.
I personally won't suggest either, and here why (besides what I mentioned above), and what I suggest to do:
First of all, highly skilled programmers are harder to replace, so besides the payrise you get, you are also securing a more stable position for yourself inside this company, not mentioning that you get more leverage when switching jobs.
Secondly, you might be only serving a beginner's gap. "Keep current" isn't some extreme request for developers nowadays considering how fast technology is evolving (in fact I would argue C++ is on the slower side), it all depends on the level of requirement of your company. From the list you provided in question (C++11, C++14/17, protocol buffers, and Agile). All the books seems to be more like a bump for a new-comer rather than some continuous task. There's no five new versions of C++ every year, protocol buffers are very low level and basic technology, and Agile, well, despite it's been wrongly used somewhere in the industry, is still some good soft skill that stay with you forever.
I would suggest you to seek for help from colleague who's been in this position for a couple of years and ask for their readlist. I could expect that your reading material will be much on leisure and informative-only side after you been through your 6 months gap. After all, you seems to be on early time of your career, all the books you listed doesn't seems be something you just learn and forget, they are going to be in your armory as long as you are staying inside the same industry.
And of course, if reading is not your cup of tea, as long as your company doesn't require you to write some reading report something, you can always talk to your boss about different kind of training to get through your gap.
Hey boss, I know the new position need me to be familiar with C++14/17, I found a good course online just about C++14/17 by [Name of some MVP], you know English is not my first language and it's much easier for me to watch a video tutorial, do you mind if it take it?
Hey boss, there's a small workshop about Agile in the town, can I attend?
Will leave much better image for you, and also help you learn in a way you prefer.
And after all, if you still decided that learning is not what you wanted in this job, or the weight put on you for this position is too much, shuffle your resume, and hunt for a job/company that's better suit for you. You still hold the job (either your old position or the new one) so you still have leverage, take advantage of it. There are company with good culture that allows you to learn your work-clock, you might want to look for this kind of companies.
But please keep this in mind:
In IT industry, motivated company prefer motivated developers, and unmotivated company disappears faster.
Generally speaking, you may probably have to keep yourself "current" more or less as long as you still want to work inside the IT industry, it's just about how much energy you have to put on it. I understood that people have preferences on work/personal life, but the situation "code 100% of the time" won't really last long under most circumstances.