What would you do if you receive a Better Job opportunity/Offer Just After Accepting and Starting another one, And How would You Act with your manager?
Your first 3 to 6 months on a job are usually part of your probation period, which means that you can still decide during that time whether the job suits you or not. If you happen to receive another job offer and find it more in-line with your career prospects, there is no harm in quitting your current job to take on the new one. Just make sure you remain very professional with your employer when resigning so that you don't leave on bad terms.
There's a well known saying :" Second chances are rare,so use your first chance wisely ". This saying answers your question .Why not to accept your better chance? so you won't regret it in the future. Be sure you are not being selfish if you do so.
Morally, you have to tell your current job's boss, and be completely honest about it.... Sure his response depends on his character and way of thinking, but logically he shouldn't mind, and understand your situation and respect the choice you had taken. Later, you can do him a favor upon his request, and make sure he feels complacent towards you "as a kind of compensation ".
I personally think that in this way you'll make use of your good chance, at the same time you will gain a friend,if not, at least you won't have a black mark on your professional record.