I can't progress any further in greek because it asks me to convert english phrases into greek. I can't do this on my mobile phone so what happens next. I would like to progress without having to write in Greek, will this be possible?
No, it will not be possible to continue without having to write in Greek.
Some of the first few lessons have some alternatives in Latin letters, and at one point the plan was to either ask for an automatic transliteration to be added by Duolingo developers (I think Russian has this) or to slowly convert the rest of the course by hand.
But that did not come to fruition partly because of the large amount of work involved (there are thousands of sentences, each of which can have dozens of accepted alternatives, so adding Latin alternatives to each would take very long), and partly because there isn't a standard transcription or transliteration for Greek, but instead many different competing versions of "Greeklish".
So we're currently deprecating Greeklish: existing sentences generally won't have the Greeklish taken away but it's not usually added to new sentences; and if an old sentence gets an additional alternative it'll only get it in Greek letters.
If you want to progress in Greek, you will have to learn to read and write it anyway at some point :) So the earlier the better.
Mobile devices usually ship with a Greek keyboard anyway, so it just has to be activated.
For PC/Mac, there are some links here: https://www.duolingo.com/comment/17706271