Hi Ghulam,

I assume, by L you mean the dc link inductance. The inductance never 'absorbs' power but stores some energy while transmitting power. 

To send back power to the AC grid, the other end of the inductor should have an active power source. The energy stored in the dc link can also be sent back as a transient power injection into the grid. 

The theory behind it is that after 90 deg, the controlled rectifier operates in inversion mode, where the output dc link voltage is negative since the dc link current has to remain positive, the power sent out to the dc link is negative, that means you are actually sending power back to the ac source from the dc link. This mode of operation is used in at the receiving ends of HVDC links. Sometimes it is also used to discharge the dc field windings of alternators. 

Firstly, the situation you are defining, is not called as 'rectification mode' but 'inversion mode' when the dc bus voltage polarity is reversed. Secondly, a simple R-L load does not support this situation: there must be a source of energy on the dc side, with correct polarity so that current flows through the SCR's in the forward direction only, eg a battery connected with its polarity reversed to the normal rectification mode bus voltage polarity.

Now, if the firing angle is more than 90 deg, then the delay angle of input ac current is also more than 90 deg. Let us simply assume that the fundamental current is now lagging by more than 90 deg, The input power on ac is V*I*cos where is more than 90 deg, implying power input is negative as cos is now negative. Thus, now power is flowing out and not in to the ac side input. remember that the power is now flowing out from the dc side energy source to the ac line.

Simply put the purpose of L the  inductor is to use its current maintaining ability(constantflux linkage theorem ensures current cannot be changed instantly in a single uncoupled inductor) , this allows the possibility of voltage reversal . The energy back to the source is from the active load   Term Rectification mode would be incorrect as already mentioned by Sujit K. Biswas , Probably what is intended to be conveyed is the operation is  in unidirectional current mode when speaking of four quadrant systems.

Cheers

I  would like to add ,to the previous answers,  That the energy is reversed for inversion mode,from the Dc source side to ac source side , while the benefit of L is to reduce ripple and keep current continue at same direction at both inversion and rectification mode of operations . Therefore if the indcuctor is assumed  ideal and very large the current,through the inductor, is smooth and no change in its stored energy at steady state conditions.

i would like to add a little....that the power flow from source to load is considered as positive whereas from load to source is negative.In both cases current direction remains same as there is no antiparallel diode for current reversal.For power reversal output voltage polarity is reversed at firing angle more than 90 that's why the mode is referred as inversion mode.