Can I use litmus paper to test unknown liquid that contains a concentrated strong acid?
Yes, concentrated strong acid can destroy litmus paper.

Paper is mostly cellulose, which is a carbohydrate polymer. Concentrated sulfuric acid will pull the hydrogen and oxygen out of it as water, leaving carbon behind. The indicator dye that's supposed to change color probably won't fare too well, either.

You can dilute the unknown by adding a drop or two of it to a small amount of distilled water, then use the litmus paper to check that.

A search for "concentrated sulfuric acid on paper" will yield many images and videos showing what the acid does to paper.