Short answer: Evangelicals identify the Apostle Paul as the most likely author of Romans 13:9–10 (and the whole Epistle to the Romans). They read these verses as Paul teaching that love fulfills the law.

Why evangelicals accept Pauline authorship
– The letter itself claims Pauline authorship (Romans 1:1; 16:22 names Tertius the amanuensis).
– Early Christian testimony consistently attributes Romans to Paul (e.g., Marcion used Romans in the mid‑2nd century; church fathers such as Irenaeus, Clement of Alexandria, Tertullian, Origen cite Romans).
– Strong manuscript support and circulation in the early church (e.g., papyri and the major codices contain Romans).
– Internal features — personal greetings in Romans 16, autobiographical remarks and theological continuity with Paul’s other letters — fit Paul’s life and thought.
– Evangelical scholars point out stylistic differences some critics note can be explained by the use of an amanuensis, shifts in rhetorical purpose, and the natural variety within a single author’s writings.

Dating, context, and purpose (evangelical summary)
– Common evangelical dating places Romans in the mid‑50s AD (often during Paul’s stay in Corinth on his third missionary journey).
– The letter was written to a mixed Jewish–Gentile Christian community in Rome, aiming to explain the gospel, promote unity between Jewish and Gentile believers, and prepare for Paul’s hoped visit to Rome and then to Spain.
– Romans 13 belongs to the ethical section of the letter (chapters 12–15), addressing how Christians live out the gospel in society. Romans 13:9–10 cites commandments from the Old Testament and presents love as the fulfillment of the law.

How Romans 13:9–10 fits Pauline theology (evangelical emphasis)
– The verses quote several commandments (e.g., “You shall not commit adultery; You shall not murder; You shall not steal; You shall not covet”) and then summarize: “Love does no wrong to a neighbor; therefore love is the fulfilling of the law.”
– This reflects a central Pauline theme: the ethical fruit of the gospel is love (compare Galatians 5:14; 1 Corinthians 13; Romans 5–8 on life in the Spirit). For evangelicals, Paul’s apostolic authority and inspiration mean this teaching carries normative weight for Christian conduct: true obedience to God flows from loving God and neighbor, not from mere legalism.

Objections and evangelical responses (brief)
– Some critical scholars question Pauline authorship or date; evangelicals reply that the external and internal evidence for Paul is strong and that alleged problems (style, vocabulary) have plausible explanations (use of an amanuensis, different rhetorical aims, natural variety).

If you want, I can:
– Quote Romans 13:9–10 in your preferred translation, or
– Give a short list of conservative/evangelical commentaries on Romans (e.g., Douglas J. Moo, John Stott, Leon Morris, F. F. Bruce) for further reading.