<p>We derive predictions for the hadronic matrix elements of radiative semileptonic decays of beautiful hadrons within Heavy Quark Effective Theory (HQET), relevant for future measurements at Belle II and LHCb. Our study considers Λ_<i>b</i> → Λ_<i>c</i>, <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math display="inline"> <msubsup> <mi mathvariant="normal">Λ</mi> <mrow> <mi>c</mi> <mn>1</mn> </mrow> <mfenced close=")" open="("> <mo>∗</mo> </mfenced> </msubsup> </math></EquationSource> <EquationSource Format="TEX">\( {\Lambda}_{c1}^{\left(\ast \right)} \)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math display="inline"> <mover accent="true"> <mi>B</mi> <mo stretchy="true">¯</mo> </mover> <mo>→</mo> <msup> <mi>D</mi> <mfenced close=")" open="("> <mo>∗</mo> </mfenced> </msup> </math></EquationSource> <EquationSource Format="TEX">\( \overline{B}\to {D}^{\left(\ast \right)} \)</EquationSource> </InlineEquation>, <i>D</i>^** transitions. The symmetries of HQET highly constrain the number of structure-dependent form factors in all cases. In the soft and sub-leading soft regions, all the form factors are fully determined in terms of non-radiative Isgur-Wise functions and the magnetic dipole moments of the heavy hadrons. The structure of higher order corrections is also briefly discussed.</p>