...and appeal lapsed

Hi, I'm looking for advice, having received the content of a PIP response to my appeal against a PIP decision.

Specifically, I'm trying to find out what my position is, when the DWP make an offer of points that qualify a claimant for the standard award of PIP in both categories, having previously denied the claimant sufficient points to qualify, in response to my appeal submission.

That sounds like a real mouthful, so I'll break it down a little:

I was previously awarded just 2 points for my claim, but having reconsidered my evidence, on appeal, the DWP have responded with awards for 8 and 9 points, which gets me a standard award, but they have not considered pain and discomfort. What is more, they've laid out that they haven't, buy saying in their response that "A claimant must be able to carry out and activity safely, repeatedly and within a reasonable time period". This is reflected in the descriptors they've chosen, so it's easily established that they haven't considered 'to an acceptable standard' or the rulings on how this should be interpreted, understanding that pain and discomfort are not acceptable.

As a result, they suggest that if I want to accept the revised award, I should call them:
"Should he wish to accept this offer, then he should contact the DWP helpline on 0800 1214433 and the appeal lapsed"

So, I understand that they are making me an offer, to pay me the standard award, but also to end the appeal process.
They also say the following:
" The Decision Maker's revising decision would be in your favour, but it is considered that it does not fully address the issue, which is the subject of the appeal. I have therefore not revised the decision, so as to prevent the appeal from lapsing".

From where I stand, it looks as though this changes my position from having no award, to getting a standard award, but only on the condition that the appeal is lapsed. I'm not sure that this is the case and I'm not sure how to proceed.
It seems logical to me that I 'should ' be able to claim what I have been offered and continue with the appeal on the basis that I should expect consideration to include 'reliable, meaning to an acceptable standard, including that pain and discomfort are not acceptable'. I've cited the appropriate cases in my appeal response and I wish to continue on that basis, but if I can, I could really do with the lesser award in the meanwhile.

Just to make matters a little more complicated, I made a fresh claim, after I sent the original claim to appeal, this time informed by benefitsandwork.co.uk. The DWP have included this in evidence for the appeal. They say they have reviewed it, but they also say they have not processed the claim. This might imply that the appeal decision for the first claim, might be said to encompass the second claim material, and perhaps therefore, judge also the second claim.

So my questions are,:
can I accept the award granted to me without lapsing the appeal?
If so, how do I make sure that the appeal is not lapsed?