OC 6: VARIANT PRAYER CUSTOMS
Since there are communal variations in prayer texts (nusach) and in other prayer- related customs, a convert may theoretically adopt those of any community that they wish as long as they remain loyal and consistent within this choice. However, if one converts in a place with a well-established, prayer text (nusach) and collective set of customs (minhagim), then the convert must adhere to those. (Generally a convert should have thought about this issue prior to conversion and should have a community in mind to join with its customs.)
OC 25: DONNING TEFILLIN AFTER CONVERSION
When a person becomes Jewish, the convert is subject only to those commandments which are in effect at the time of the conversion. However, even if the convert has already performed such a commandment that day as a Gentile, the convert must repeat it in order to fulfill their obligation as a Jew. Therefore: inasmuch as the time frame for donning tefillin is the entire day, a ger who converts in the afternoon must don tefillin (again, if done already prior to the conversion).
OC 39: THE VALIDITY OF TEFILLIN WRITTEN BY SOMEONE WHO REVERTS TO THEIR OLD FAITH OUT OF FEAR
A convert can work as a sofer stam (religious scribe), and all their work is valid to the same degree as those of a born-Jew. There are those who claim that a convert who apostatizes out of fear of governmental authorities can write a valid sefer torah, tefillin, and mezuzot. Since the convert is rejecting the faith only in order to save their life, the convert is viewed as a full-fledged Jew. (Furthermore: there are many who claim that the rules regarding a convert who had reverted to their faith of birth are more lenient than for a born-Jew who had converted out of fear of death.)