I found this article.It is very helpful for whom may think of moving out os current state for Job searching.

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If you are receiving unemployment insurance benefit payments when you move out of state to look for work, you may still receive unemployment payments from the state that awarded the benefit. The law of the state that awarded the benefit applies just as it would for in-state workers. A worker’s eligibility, amount and duration of unemployment benefit payments, and disqualifications will be determined by the state where wages were paid and earned.

Calculating Unemployment Benefits: Your Former State

Each individual state has laws that help determine benefit entitlements for unemployed workers. Some states calculate benefit payments based on a multiple of weekly benefit amount, while others use methods based on a flat qualifying amount or the weeks/hours of employment. When your state computes your monetary eligibility for benefits, it determines the duration of benefits, meaning how long benefits can be collected, in addition to calculating the weekly benefit amount. Several states establish uniform durations of 26 weeks for all workers who meet the qualifying-wage requirements. Other states provide benefit durations between 26 to 30 weeks. The most common duration overall, however, is 26 weeks. If you move out of state at the beginning or during your duration of benefits period, you will continue to receive the benefits for the maximum amount of time allowed in your state.

Collecting Unemployment Benefits in Your New State

Although the Unemployment Insurance System is run by individual states, all states are members of the Interstate Reciprocal Benefit Payment Plan. If you prefer to apply for benefits in your new state, you have that right. However, the unemployment laws of the former state will still govern your benefit payment calculations. You also need to start looking for work immediately after moving to a new state and report all job inquiries within each weekly filing.

Some states will allow you to move your unemployment benefits without participating in the Interstate Reciprocal Benefit Payment Plan. In these states, you only need to contact state authorities prior to your move. Your former state of residence will then arrange to transfer your benefits to be paid through the new state's unemployment insurance authority.