Might kept begging his parents for a cell phone they agreed he could use his allowance to buy one which transition word or phrase would go at the beginning of the second sentence to show how the ideas are connected

Therefore

In addition,

The transition word or phrase that could be used at the beginning of the second sentence to show how the ideas are connected is "finally".

To understand why "finally" is appropriate, let's break down the context and logical flow of the ideas:

1. The first sentence states that Might kept begging his parents for a cell phone.
2. The second sentence introduces a new development: his parents agreed he could use his allowance to buy one.

The word "finally" helps to indicate that after Might's persistent begging, a resolution has been reached. It connects the two ideas to show that the desired outcome has been achieved.