Is the Adhan with 13 phrases (repeated twice without tarji') valid, and what should one do if they wish to gain the reward of repeating after the mu'adhdhin in this case?

Several forms of the adhan have been narrated, all of which are valid:

1. Thirteen phrases: The takbir twice at the beginning, without tarji' (this is the madhhab of Malik when omitting tarji', and some Malikis, and it is narrated from Ibn Umar).

2. Seventeen phrases: The takbir twice at the beginning, with tarji' (this is the madhhab of Malik, and it is narrated from Abu Mahdhurah).

3. Fifteen phrases: The takbir four times at the beginning, without tarji' (this is the madhhab of Abu Hanifah and Ahmad, and it is Bilal's adhan).

4. Nineteen phrases: The takbir four times at the beginning, with tarji' (this is the madhhab of Shafi'i, and it is narrated from Abu Mahdhurah).

Tarji' is to recite the two Shahadas twice in a low voice, then raise them twice. All of these forms are sunnah, and it is permissible to make the adhan with any of them.