Interesting question. I'll take a stab at answering. But you might want to repost this as a "Litigation" question. That way, you will get all the civil litigators responding to your question.
Short answer: Yes, assuming you do it correctly.
Long answer: You have the following issues. First, this is inadmissible hearsay, so you need to figure out if it fits in an exception to the hearsay rule. You can probably get around the hearsay rule because you are not trying to enter it into evidence for the truth of the matter asserted.
Second, you have the "chain of custody" issue. In legaleze, you need to "lay the foundation" of admitting the recording into evidence. There are various ways to do this. The simplest (but riskiest) is to wait until the hearing and then just testify that you transferred the call from one number to the other, etc. etc.
Third, get a copy of the phone log (showing the "from" and "to" phone numbers). Even if the recording itself is not admitted, you still have the paper phone log. Since all you need to show is that the other person called your phone, that is probably sufficient. Of course, the other person might claim that someone else used his phone. It would be best to have both the recording and log.
Fourth, I suggest transcribing each of the phone calls onto separate pieces of paper. You can try to get those admitted into evidence as well.
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