united-states
The most likely result is that B holds the assets of A as a nominee and A is taxed on those assets, and that the transfers from B to A are disregarded.
It could be taxed as an annuity or as a grantor retained annuity trust or grantor retained unitrust, depending upon how the distributions back to A are calculated.
The absence of a written contract is not material. Trust and nominee arrangements are not required by law to be in writing.
But, given the effort of A and B to evade taxation in a misleading way (and the fact that they were presumably reporting the transaction inconsistently with economic reality and consistent with their fraudulent scheme), most likely A and B would also be prosecuted for criminal tax fraud, in addition to punitive tax penalties on any underpayment of tax or underreporting of income.
It is also likely that the transfers were for some additional non-tax purpose, for example, to escape the claims of creditors, in which case the transfer would be fraudulent transfers under the Uniform Fraudulent Transfer Act. Depending upon the circumstances, there could have also been other civil or criminal fraud or regulatory offenses committed.