Consider engineering disciplines A and B. Assume that the mathematical skills required for A and B are same. Let us say I am a fresh Ph.D pass out in A and say I did a reasonable one compared to the standards. My experience in B is limited to some coursework, but I believe I do have the ability to do research in it. I wish to work in a company in B. Now one of them has shown some interest in me and has asked for a telephonic interview. How should I go about justifying my interest in B though I did a Ph.D in A?
You justify your interest in B like you justify your interest in any field, by simply explaining why you like it. They might not ask you to justify your interest though, they might simply ask you to explain why you want that particular job and what skills you can bring to it.
If you have a PhD, you have learned how to learn and research independently. Its not unusual for people to end up working in something different to what they were doing in their PhD. I know a professor of computer science whose PhD is in pure mathematics.
You should do some reading in B so that you are familiar with both the basic concepts i.e. refresh your coursework if it was completed a while ago. Also, read the latest research in B; if its not an academic job they may not require this but because you have a PhD they may assume you have done it.
If you are interested in B, be prepared to expand on why you are interested in B. On the other hand:
Why should you ask "how should I justify my interest in B"? Is there anything about your interest in B that you should feel apologetic for and that you thus have to justify? You have the right to your preferences to the same extent that everybody else does. You have the same right to change your mind, adjust your preferences and pivot according to them that everybody else does. Without apology.
They're more likely to be interested, and to make you an interesting offer, if you can explain how you intend to bring your knowledge of A into B's field and develop something new from the combination.
("I'm bored to death of A" worries me a bit, though, given how much time and effort you've invested in it.)