  We investigate twisted electrons with a well defined orbital angular
momentum, which have been ionised via a strong laser field. By formulating a
new variant of the well-known strong field approximation, we are able to derive
conservation laws for the angular momenta of twisted electrons in the cases of
linear and circularly polarised fields. In the case of linear fields, we
demonstrate that the orbital angular momentum of the twisted electron is
determined by the magnetic quantum number of the initial bound state. The
condition for the circular field can be related to the famous ATI peaks, and
provides a new interpretation for this fundamental feature of photoelectron
spectra. We find the length of the circular pulse to be a vital factor in this
selection rule and, employing an effective frequency, we show that the
photoelectron OAM emission spectra is sensitive to the parity of the number of
laser cycles. This work provides the basic theoretical framework with which to
understand the OAM of a photoelectron undergoing strong field ionisation.
