There is a considerable amount of correspondence between Augustine and Jerome which is extant. Although the Latin texts are not aviailable on the Internet, English translations can be easily found. Below are some excerpts from letters that Augustine wrote to Jerome.
[complete English translation of the letter can be found at New Advent]
section 2. We therefore, and with us all that are devoted to study in the African churches, beseech you not to refuse to devote care and labour to the translation of the books of those who have written in the Greek language most able commentaries on our Scriptures. You may thus put us also in possession of these men, and especially of that one whose name you seem to have singular pleasure in sounding forth in your writings [Origen]. But I beseech you not to devote your labour to the work of translating into Latin the sacred canonical books, unless you follow the method in which you have translated Job, viz. with the addition of notes, to let it be seen plainly what differences there are between this version of yours and that of the Septuagint, whose authority is worthy of highest esteem. For my own part, I cannot sufficiently express my wonder that anything should at this date be found in the Hebrew manuscripts. which escaped so many translators perfectly acquainted with the language. I say nothing of the Septuagint, regarding whose harmony in mind and spirit, surpassing that which is found in even one man, I dare not in any way pronounce a decided opinion, except that in my judgment, beyond question, very high authority must in this work of translation be conceded to them. I am more perplexed by those translators who, though enjoying the advantage of labouring after the Septuagint had completed their work, and although well acquainted, as it is reported, with the force of Hebrew words and phrases, and with Hebrew syntax, have not only failed to agree among themselves, but have left man), things which, even after so long a time, still remain to be discovered and brought to light. Now these things were either obscure or plain: if they were obscure, it is believed that you are as likely to have been mistaken as the others; if they were plain, it is not believed that they [the Septuagint could possibly have been mistaken. Having stated the grounds of my perplexity, I appeal to your kindness to give me an answer regarding this matter.
[complete English translation of the letter can be found at New Advent]
4. For my part, I would much rather that you would furnish us with a translation of the Greek version of the canonical Scriptures known as the work of the Seventy translators. For if your translation begins to be more generally read in many churches, it will be a grievous thing that, in the reading of Scripture, differences must arise between the Latin Churches and the Greek Churches, especially seeing that the discrepancy is easily condemned in a Latin version by the production of the original in Greek, which is a language very widely known; whereas, if any one has been disturbed by the occurrence of something to which he was not accustomed in the translation taken from the Hebrew, and alleges that the new translation is wrong, it will be found difficult, if not impossible, to get at the Hebrew documents by which the version to which exception is taken may be defended. And when they are obtained, who will submit, to have so many Latin and Greek authorities: pronounced to be in the wrong? Besides all this, Jews, if consulted as to the meaning of the Hebrew text, may give a different opinion from yours: in which case it will seem as if your presence were indispensable, as being the only one who could refute their view; and it would be a miracle if one could be found capable of acting as arbiter between you and them.
