LLC Purchase, Accrual v cash, quickbooks entry

I have a client who purchased a single member LLC. He paid 250k for the interest in the LLC. He did not change the EIN. The contract speaks nothing on the assumption of liabilities but based on the way he is handling business he assumed all liabilities and outstanding contracts. He also kept the assets of the business. (the contract list a few of these assets) He basically stepped into the old owners shoes. I have a few questions that I would like to get a another opinion.
1. The new owner wants to keep books on an accrual basis. We have no idea how the prior owner was keeping books. There are several contracts that had billings in 2015 but were not paid until 2016. This has a huge impact with accrual vs cash. Can they just decide to do accrual basis bookkeeping without knowing what the prior owner did? Would they not pick up in the books where the prior owner left off since he assumed ownership? If they choose to do accrual but the prior owner was cash basis then there would be income that would not be reported on either of their books.
2. How would the 250k paid be allocated? Would i have to allocate between assets, liabilities, etc. Or would this be put on the books as a name "interest" only purchase?
3. Lastly, the company will sign a contract lets say June for 18,000 and then in Oct they will have done some work for the contract. In Oct they issue a billable summary to there customer requesting payment for the work done so far. It reduces the overall contract price. In Jan the following year the client finally receives payment for the Oct. billing. I want to make sure that I am entering this correctly in to quickbooks. I do not enter the 18,000 as they have not earned this money. I wait until the client issues a billable summary and enter an invoice. This puts on the books what they have earned and then when payment comes in Jan. i post the payment received against said invoice. For now lets say they get their way and they are on an accrual basis. When the invoice is entered that post the income to their profit and loss statement. Would this be right for posting or would i need to post the full 18,000 when the contract is signed?

It sounds like you are not certain from your reading of the contract whether this was a stock sale or an asset sale. (You say that "based on the way he is handling business...) Before you do anything else this needs to be determined. If you aren't sure perhaps discuss with the client's lawyer? If it is a stock sale and he is stepping into the prior owner's shoes, he needs the prior year tax returns and all of the books and records. What if he is audited for a prior year? How would he support the tax positions the prior owner took?

I finally got my hands on the contract (not just what the client had on hand) and it was a member interest purchase so he purchased the prior owners interest in the company. Which was a disregarded entity.

IRC section 1060.