Why doesn't change in accounts receivable on balance sheet match cash flow statement?

I'm not an expert, but here is my best hypothesis. On Microsoft's (and most other company's) cash flow statements, they use the so-called "indirect method" of accounting for cash flow from operations. How that works, is they start with net income at the top, and then adjust it with line items for the various non-cash activities that contributed to net income. The key phrase is that these are accounting for the non-cash activities that contribute to net income. If the accounts receivable amount changes from something other than operating activity (e.g., if they have to write off some receivables because they won't be paid), the change didn't contribute to net income in the first place, so doesn't need to be reconciled on the cash flow statement.

Increase in A/R in balance sheet includes the A/R of acquired businesses.

Change in A/R in cash flow statement might say "excluding effects of business acquisitions".

It is difficult to reconcile historical balance sheets with historical cash flow statements because there are adjustments that are not always clearly disclosed. Practitioners consider activity on historical cash flow statements but generally don't invest time reconciling historical accounts, instead focusing on balancing projected balance sheets / cash flow statements. If you had non-public internal books, you could reconcile the figures (presuming they are accurate).

In regards to Mike Haskel's comment, there's also a section pertaining to operating capital, not just effects on net income.

QUICK ANSWER

What @Mike Haskel wrote is generally correct that the indirect method for cash flow statement reporting, which most US companies use, can sometimes produce different results that don't clearly reconcile with balance sheet shifts. With regards to accounts receivables, this is especially so when there is a major increase or decrease in the company's allowances for doubtful accounts.

In this case, there is more to the company's balance sheet and cash flow statements differences per its accounts receivables than its allowances for doubtful accounts seems responsible for. As explained below, the difference, $1.25bn, is likely owing more to currency shifts and how they are accounted for than to other factors.

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DIRTY DETAILS

Microsoft Corp. generally sells to high-quality / high-credit buyers; mostly PC, server and other devices manufacturers and licensees. It hence made doubtful accounts provisions of $16mn for its $86,833mn (0.018%) of 2014 sales and wrote off $51mn of its carrying balance during the year.

Its accounting for "Other comprehensive income" captures the primary differences of many accounts; specifically in this case, the "foreign currency translation" figure that comprises many balance sheet accounts and net out against shareholders' equity (i.e. those assets and liabilities bypass the income statement). The footnotes include this explanation:

Assets and liabilities recorded in foreign currencies are translated at the exchange rate on the balance sheet date. Revenue and expenses are translated at average rates of exchange prevailing during the year. Translation adjustments resulting from this process are recorded to other comprehensive income (“OCI”)

What all this means is that those two balance sheet figures are computed by translating all the accounts with foreign currency balances (in this case, accounts receivables) into the reporting currency, US dollars (USD), at the date of the balance sheets, June 30 of the years 2013 and 2014.

The change in accounts receivables cash flow figure is computed by first determining the average exchange rates for all the currencies it uses to conduct business and applying them respectively to the changes in each non-USD accounts receivables during the periods.

For this reason, almost all multinational companies that report using indirect cash flow statements will have discrepancies between the changes in their reported working capital changes during a period and the dates of their balance sheet and it's usually because of currency shifts during the period.