Can my friend pay the state tax return on behalf of me by his check?

[KrisD]

You could send the check with your voucher and make sure your name and your social security number and "Tax year 2018" are written in the memo. HOWEVER, it could get messy. IF the friend is paying your taxes for you, it would need to be considered a "gift" to not be additional (and taxable) income for you to claim on your 2019 return next year. 

The best thing to do is have a money order issued rather than using a check.