You have included cash which Motorola had when getting acquired but have conveniently ignored their short term debts (current liabilities) which they were liable to pay. A better number to look at is net working capital.
You're absolutely right that one needs to adjust for short-term liabilities since some of that cash would have gone to pay them (Longer-term liabilities would likely continue on to Lenovo). As big a question in this case is the amount of cash that will be in Motorola when Lenovo acquires it and was in their set-up box business when it was sold.
Unfortunately, the comment isn't editable so I'll add more detail here. The more accurate number is $3.32B in cash and equivalents less ($3.57B in current liabilities - $2.97 in current non-cash assets). This totals $2.72B.
However, I understated the tax benefit. Motorola had a $2.5B reserve against their tax assets since they weren't profitable, which is $0.8B less than my original estimate. So the total error from these two items is an understatement of Google's recoveries by $0.52B, which means they recovered about $10.9B of $12.5B.
Note that there are likely other errors still present in this new calculation due to both lack of information and less than thorough research.
